Modules Definition and 224 Threads

Broadly speaking, modularity is the degree to which a system's components may be separated and recombined, often with the benefit of flexibility and variety in use. The concept of modularity is used primarily to reduce complexity by breaking a system into varying degrees of interdependence and independence across and "hide the complexity of each part behind an abstraction and interface". However, the concept of modularity can be extended to multiple disciplines, each with their own nuances. Despite these nuances, consistent themes concerning modular systems can be identified.

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  1. Math Amateur

    MHB Left modules notation with a left subscript?

    I am reading Berrick and Keating's book on rings and modules. Berrick and Keating indicate a right module over a ring R as M_R, but in a left module the subscript is to the left ... can someone help me with the Latex script to achieve this? An example of "left-subscript" notation appears in...
  2. Math Amateur

    MHB Proof of Fourth or Lattice Isomorphism Theorem for Modules

    Dummit and Foote give the Fourth or Lattice Isomorphism Theorem for Modules on page 349. I need some help with the proof of Fourth or Lattice Isomorphism Theorem for Modules ... hope someone will critique my attempted proof ... (I had considerable help from the proof of the theorem for groups...
  3. Math Amateur

    MHB Fourth or Lattice Isomorphism Theorem for Modules - clarification

    Dummit and Foote give the Fourth or Lattice Isomorphism Theorem for Modules on page 349. The Theorem reads as follows:https://www.physicsforums.com/attachments/2981In the Theorem stated above we read: " ... ... There is a bijection between the submodules of M which contain N and the submodules...
  4. Math Amateur

    MHB Modules - Decomposibiity of abelian groups

    I am reading An Introduction to Rings and Modules With K-Theory in View by A.J. Berrick and M.E. Keating (B&K). I need help with understanding Example 2.1.3 (ii) (page 39) which concerns L as a submodule of the quotient module \mathbb{Z}/p^r \mathbb{Z} ... ... Example 2.1.3 (ii) (page 39)...
  5. Math Amateur

    MHB Indecomposable modules - example from Berrick and Keating

    I am reading An Introduction to Rings and Modules With K-Theory in View by A.J. Berrick and M.E. Keating (B&K). At present I am focussed on Chapter 2: Direct Sums and Short Exact Sequences. Example 2.1.2 (i) on pages 38-39 reads as follows:https://www.physicsforums.com/attachments/2957 In the...
  6. Tesladude

    Combining modules to transmit video signal for RC car

    I don't see why not but is there any reason that i could not use these modules http://www.ebay.com/itm/121370353437?ssPageName=STRK:MEWAX:IT&_trksid=p3984.m1423.l2649 to make a wireless link between this camera and screen...
  7. Math Amateur

    MHB Basic Question on Modules - Dummit and Foote Chapter 10

    I am reading Dummit and Foote Chapter 10: Introduction to Module Theory. After defining modules and giving some examples, D&F state the following: "We emphasize that an abelian group M may have many different R-module structures even if the ring R does not vary ... ... " I am puzzled by this...
  8. Math Amateur

    Direct Products of Modules - Bland - Proposition 2.1.1 and its proof

    I am reading Paul E. Bland's book, Rings and Their Modules, Section 2.1: Direct Products and Direct Sums. I have a question regarding the proof of Proposition 2.1.1 Proposition 2.1.1 and its proof (together with with a relevant preliminary definition) read as follows: As can be seen in the...
  9. Math Amateur

    Direct Products of Modules - Bland - Rings and Their Modules

    I am reading Paul E. Bland's book, Rings and Their Modules. In Section 2.1: Direct Products and Direct Sums, Bland defines the direct product of a family of modules. He then, in Proposition 2.1.1 shows that there is a unique module homomorphism (or R-Linear mapping) from any particular R-module...
  10. Math Amateur

    MHB Direct Products of Modules - Bland - Proposition 2.1.1 and its proof

    I am reading Paul E. Bland's book, Rings and Their Modules, Section 2.1: Direct Products and Direct Sums. I have a question regarding the proof of Proposition 2.1.1 Proposition 2.1.1 and its proof (together with with a relevant preliminary definition) read as follows...
  11. Math Amateur

    MHB Direct Products of Modules - Bland - Rings and Their Modules

    I am reading Paul E. Bland's book, Rings and Their Modules. In Section 2.1: Direct Products and Direct Sums, Bland defines the direct product of a family of modules. He then, in Proposition 2.1.1 shows that there is a unique module homomorphism (or R-Linear mapping) from any particular R-module...
  12. Sudharaka

    MHB Finitely Generated Modules and Artinian Rings

    Hi everyone, :) Here's another question that I am struggling to complete. If you have any hints or suggestions for this one, I would be so grateful. :) Question: Let $S\subseteq R$ be rings and assume that $R_S$ is a finitely generated $S$-module. If $S$ is Artinian prove that $R$ is also...
  13. Sudharaka

    MHB Free and Finitely Generated Modules

    Hi everyone, :) Want to confirm my understanding about Free and Finitely Generated modules. I want to know whether the following ideas are correct. Thank you for all your help. :) 1) Is every free module a finitely generated module? No. Because a free module may have an infinite basis. So we...
  14. J

    What is the best topology for adding surge protection to Ethernet PHY?

    Hi, Guys I have a B78476A8135A003 Magnetic Module from EPCOS and I want to add a surge protector either on the TJ45 connector side or the Ethernet PHY side. I can't decide which way is more beneficial. Here is the topology: Ethernet PHY : B78476A8135A003 : Surge Protector (SLVU2.8-4) ...
  15. T

    Fortran How to Resolve Compilation Errors with Fortran 90/95 MODULEs?

    Hi! I require help in writing a code where I want to put FUNCTION definitions in one module and INTERFACEs to the functions (as I use assumed-shape arrays in the functions) in another. But I get multiple errors when trying to compile. Could anyone assist me in solving this problem? Please see...
  16. Z

    Optional Physics modules - decision time

    I was wondering if anyone would have an opinion on which four of the following final year Physics modules would be most useful to have completed post-graduation? Solid State Physics Atomic and Molecular Physics Physics in Medicine Nuclear and Fundamental Particle Physics Electromagnetic...
  17. Math Amateur

    MHB Direct Products and Sums of Modules - Notation - 2nd Post

    I am reading John Dauns book "Modules and Rings". I am having problems understanding the notation of Section 1-2 Direct Products and Sums (pages 5-6) - see attachment). In section 1-2.1 Dauns writes: ================================================== ====== "1-2.1 For any arbitrary...
  18. Math Amateur

    MHB Direct Products and Sums of Modules - Notation

    I am reading John Dauns book "Modules and Rings". I am having problems understanding the notation in section 1-2 (see attachment) My issue is understanding the notation on Section 1-2, subsection 1-2.1 (see attachment). Dauns is dealing with the product \Pi \{ M_i | i \in I \} \equiv \Pi M_i...
  19. O

    MHB Prove (I + J)/J is isomorphic to I(R/J) as R modules

    Let R be a commutative ring and I, J be ideals of R. Show that (I + J)/J is isomorphic to I(R/J) as R modules. I am having trouble coming up with the explicit isomorphism. For I(R/J) I know any element can be expressed as i(r + J) = ir + J by definition of the action of R on R/J. As for (I +...
  20. G

    Ring with Infinitely Many Simple Modules

    Homework Statement Give an example of a ring R with infinitely many non-isomorphic simple modules. The Attempt at a Solution I was thinking of setting R=\mathbb{Z}_{p_1}\times \mathbb{Z}_{p_2}\times \mathbb{Z}_{p_3}\times \cdots where p_1,p_2,p_3,\ldots is an infinite increasing list...
  21. S

    Schools Mathematicians opinion on university modules

    Hi, I'm wondering if anyone could suggest which out of the two below universities would give me the "better" mathematics major. By better I mean the most rigorous, the hardest and the one which will prepare me most for a phd. 1. http://www.ucl.ac.uk/maths/courses/undergraduates/ I won't be...
  22. T

    Power Electronics Modules and Vendors - Help Needed

    Dear all, I have an urgent task of finding the right experimental modules for Power Electronics Course in my university, for undergrad. level. Could you please provide me with a list of good and reliable vendors who can provide me with modules that can enable the students to perform...
  23. M

    Selecting Modules for Physics Studies - Which Ones to Choose?

    I posted a similar thread a few months ago but the available modules has changed. I'm interested in space time, black holes, general rel, field theory, quantum mechanics. I can choose 6 from this MA3413 Group representations I Lecturer: Prof. Vladimir Dotsenko MA3421 Functional...
  24. A

    Comparing definitions of groups, rings, modules, monoid rings

    Hi, I wanted to see what people think about my current viewpoint on recognizing structures in abstract algebra. You count the number of sets, and the number of operations for each set. You can also think about action by scalar or basis vectors. So monoids groups and rings have one set...
  25. Matt atkinson

    Need help Second year theoretical physics modules

    Hello, thank you for taking a look at this thread. Here is my dilemma, I can chose 30 credits from various math and physics courses (each worth 10) for my second year, but I've decided to do maths as the rest of my modules are all physics but there are so many I have no idea what maths modules...
  26. A

    Can a Non-Zero Tensor Product of Modules Be Zero?

    I'm reading about tensor product of modules, there's a theorem in the book that leaves parts of the proof to the reader. I've attached the file, I didn't put this in HW section because first of all I thought this question was more advanced to be posted in there and also because I want to discuss...
  27. M

    Modules to Choose for Specializing in General Rel.

    Hey, these are the modules I have to choose for next year, still subject to change, so the available modules might not be the same when the form has to be in, but whatever. I want to specialise in things like General Rel, black holes, space time, etc... I can choose 6 from the following...
  28. W

    Having trouble working with modules

    Hi guys, Basically I'm playing around with modules at the moment, and I can't work out why we can't have the group of integers as an F-module (F a field), where the left action is the identity. i.e F x Z ----> Z where we have f.z = z f in F, z in Z If this were possible, then Z would be a...
  29. R

    Gap between the plates of a Thermal Electric Modules

    Dear Experts Does anyone know how big can we extend the gap between the 2 plates? Thanks. Regards Ramone
  30. G

    Quotients of direct sums of modules

    Hi, I keep seeing indirect uses of a result which I think would be stated as follows: If a module M over the unital associative algebra A is written M\cong S_1\oplus\cdots\oplus S_r (where the S_i are simple modules), then in any comosition series of M, the composition factors are, up to...
  31. O

    Exploring the Equivalence of FG-Modules and Group Representations

    There is a Theorem that says FG-Modules are equivalent to group representations: "(1) If \rho is a representation of G over F and V = F^{n}, then V becomes an FG-Module if we define multiplication vg by: vg = v(g\rho), for all v in V, g in G. (2) If V is an FG-Module and B a basis of V...
  32. A

    Please help me to choose 3 rd Year Maths modules at QMUL

    Dear Sir,Madam,Friends 1)I did well in Number theory and found it easy. will " combinatorics" module be easy for me? 2) I have not put any time into studying Statistics & even did not bother to pass intro to Stat module. will Actuarial maths be easy for me ? does actuarial maths have a lot...
  33. P

    How Do You Integrate Multiple Verilog Modules into One?

    I have written many verilog codes and I need to make all of them in a single module. Can anyone help me?
  34. M

    Word for one-to-one correspondence between ideals and modules of an algebra

    I do not know if this is a common/standard construction, so here is my motivation for this question. From http://arxiv.org/abs/1002.1709" page 29: Is there a word for when there is such a one-to-one correspondence?
  35. K

    Vector spaces as quotients of free modules

    Homework Statement Let R be a commutative ring, and let F = R^{\oplus B} be a free R-module over R. Let m be a maximal ideal of R and take k = R/m to be the quotient field. Show that F/mF \cong k^{\oplus B} as k-vector spaces. The Attempt at a Solution If we remove the F and k...
  36. K

    Finitely generated modules as free modules

    I'm reading up on the classification of finitely generated modules over principal ideal domains. In doing so, I continuously come up on the statement "Let M be a finitely generated, free R-module." My question is, is this statement redundant? It seems to me that all finitely generated R-modules...
  37. K

    What is the Presentation and Determination of Modules over a Field?

    Homework Statement Let k be a field and k[x] be the set of polynomials over that field. Given that M is a module with presentation \begin{pmatrix} 1+ 3x & 2x & 3x \\ 1 + 2x & 1+ 2x -x^2 & 2x \\ x & x^2 & x \end{pmatrix} determine M. Homework Equations One can apply elementary row and...
  38. B

    Orthogonal Subgroups : on Modules?

    Hi, All: I have seen Orthogonal groups defined in relation to a pair (V,q) , where V is a vector space , and q is a symmetric, bilinear quadratic form. The orthogonal group associated with (V,q) is then the subgroup of GL(V) (invertible linear maps L:V-->V ), i.e., invertible matrices...
  39. M

    Modules for Theoretical Physics

    Right so I'm a math major but what I really want to be is a theoretical physicist. 3rd and 4th year is when everything gets very specified, and I'm wondering which of the following modules would be most useful for that path? Here are the modules. Only 6 can be chosen from each term...
  40. N

    Modules over an Integral Domain

    Homework Statement Let R be a ring with no zero divisors such that for any r,s\in R, there exist a,b \in R such that ar+bs=0. Prove: R=K \oplus L implies K=0 or L=0. Homework Equations Definition of direct sum of modules, integral domain... The Attempt at a Solution I didn't know...
  41. T

    A program consists of two modules

    Question: A program consists of two modules. The number of errors X in the first module and the number of errors in the second module have the joint distribution: P(0,0) = P(0,1) = P(1,0) = 0.20 P(1,1) = P(1,2) = P(1,3) = 0.10 P(0,2) = P(0,3) = 0.05 Find i) the marginal distribution...
  42. Z

    MPPT analysis in parallel and series configration with similar solar modules

    hello! Hope you all will be at quiet ease. I am looking for the guidance to observe the performance analysis of MPPT (Maximum power point Tracker) in parallel and series configuration with similar solar modules. I have two solar modules each having the following rating: - Maximum power...
  43. H

    Torsion-free modules over a Discrete Valuation Ring

    Let R be a discrete valuation ring with fraction field F. I believe it's straightforward to show that any torsion-free module M with the property that M \otimes_R F is a finite dimensional F-vector space is of the form R^m \oplus F^n. What if M \otimes_R F is infinite dimensional?
  44. D

    Unique representation in graded modules

    In atiyah's book on commutative algebra page 106 it says that elements in graded modules can be written uniquely as a sum of homogeneous elements. More precisely: If A = \oplus^{\infty}_{n=0} A_n is a graded ring, and M = \oplus^{\infty}_{n=0} M_n is a graded A-module, then an element y \in...
  45. J

    How to Couple Two Modules in COMSOL?

    Hi, I want to couple two different modules of COMSOL. For example u is the solution of Module 1 and I want to give 0.95*u+a as subdomain settings parameter in module 2. Here a is a vector. I have succeeded with u and 0.95*u to use as subdomain settings parameter of module 2 but when I add a ...
  46. S

    Courses Choosing modules for theoretical Physics from Math Graduate Diploma course

    Choosing modules for theoretical Physics from Math Graduate Diploma course: Hi forum members, I am studying Math Graduate Diploma at Kings College london. I am going to do M.Sc Theoretical Physics next year. I need your advice in choosing Math Grad Diploma modules closely related to the...
  47. J

    How do you study for engineering modules?

    how do u guys handle college engineering modules? personally i find them very difficult as i usually take quite a bit of time to grasp some of the concepts presented. I'm studying mechanical engineering, and i have problems with mathematics, mechanics and dynamics. just wondering if any of u...
  48. G

    Effects of Irradiance and Temperature on Solar Modules

    Can you please suggest me some books to read on this topic? It's for my final year project! I would much appreciate it!
  49. J

    Finitely generated modules over a PID, and applications on abelian groups

    Hello! I'm currently taking a course in group- and ring theory, and we are now dealing with a chapter on finitely generated modules over PIDs. I have stumbled across some problems that I can't really get my head around. It is one in particular that I would very much like to understand, and I...
  50. M

    Choosing the Best Mechanical Engineering Modules for Your Career

    Hello. I have to choose 2 of the above Mechanical Engineering modules and i would like to make the best choice for future jobs and better CV. 1. Engineering Materials 2. Resource Management 3. Automated Manufacturing 4. Power Hydraulics Any help? Cheers
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