module Definition and 167 Threads

In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a ring. The concept of module generalizes also the notion of abelian group, since the abelian groups are exactly the modules over the ring of integers.
Like a vector space, a module is an additive abelian group, and scalar multiplication is distributive over the operation of addition between elements of the ring or module and is compatible with the ring multiplication.
Modules are very closely related to the representation theory of groups. They are also one of the central notions of commutative algebra and homological algebra, and are used widely in algebraic geometry and algebraic topology.

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  1. P

    Finding a Basis for a Module: Techniques and Examples

    Homework Statement Given a few vectors that span a module space, how do you find a set that is a basis for this spanned space consisting of entirely different vectors to the original spanning vectors? The Attempt at a Solution I assume you find what kind of space is spanned by the...
  2. P

    R Module M is Cyclic: Isomorphic to R/(p)?

    Homework Statement If an R module M is cyclic so M=Rm with annihilator(m)=(p), p prime then can we infer that M is isomorphic to R/(p) without any more infomation?
  3. H

    Module Problem: Existence and Sub-Module of N

    Let R be a commutative ring, with subring S. Let M be an R-module. Does there exist a S-module N such that N \otimes_S R \cong M as R-modules? Preferably with N a sub-S-module of M? Even better, can we choose such modules N so that if we have an R-module homomorphism f:M --> M' it...
  4. W

    Divisibility problem cant use module just induction

    Hi all, Great forum, I have been reading some cool stuff here for about a month. Heres my question: Using induction prove that 5 divides 8^n - 3^n, n Natural Number. I know its true for n = 1, but I get stuck on the n = k+1. I don't know how to proceed from here: 8(8^k) - 3(3^k)...
  5. S

    Q as Module over Z: Proving Unfinite Generating Ability

    Hey guys, I'm self-teaching maths to preper myself for the next term of uni, so I'm reading this book on abstract algebra, and somewhere it says that R (the set of real numbers) is not finitely generated as a module over Q (set of rational numbers). Now, I can see that it's not, but i can't...
  6. P

    Difference between algebra and module?

    Obviously having been assigned two different terms indicates these two objects are different but as far as I know, algebra: vector space with the multiplication which takes two elements in vector space and give another in vector space module: vector space over ring(extending from field)...
  7. T

    Develop the algorithm as a module

    Consider the following specification: pre n >= 1 post search module(a, n, number) = FOUND(a, number) reads a, n, number changes - mem - Remark: Let i be an integer number. Then, FOUND = 0 iff a does not contain number and FOUND = i iff a[i] = number. search module is the name of...
  8. N

    Python Loading a file (module) in Python

    I have installed Python in a Windows environment and I want to load files to execute them in Python. I have tried "import testprogram.py" and it does load the program and executes it (all the program does is to print something out on the screen) but then there are error messages...
  9. S

    Which Maths Module Should I Choose?

    I'm going to take an extra module, from a choice of two, from my university's maths department next year and I was just wondering which is more interesting. The choice is Topology or Abstract Algebra.
  10. S

    G3 Trigger Module: Build Your Own High Speed Sensor

    hiya a few months ago i got a canon g3, upgrade from a eos 300. first stab in the digital world. now with non digital cams you had a shutter release input, which you could build your own sensors and whatnot for, for taking high speed pics etc etc. it was pretty much a case of applying the...
  11. T

    What is the compressibility module and why is it important in fluid mechanics?

    Hello everyone ! I'm currently working on a problem in Eugene Hecht's Physics book. It's about static fluid and the "compressibility module". I'm not sure this traduction makes sense, because my book is translated into French and I can't find the correct English expression. For those who have...
  12. D

    Prove Endomorphism Ring of Simple Module is a Field

    I spent like 6 hours trying to prove that the endomorphism ring of a simple module is a field, helping my friend with his homework. Now I'm convinced that the result is not true. By Schur's lemma, all endomorphisms of a simple module (except 0) are isomorphisms, so it's a division ring, but I...
  13. J

    Proving Module Homomorphisms: A x B to M & M to A x B

    If you can help, that would be great. Let R be a commutative ring, and A,B,M be R-modules. Prove: a) HomR(A x B, M) is isomorphic to HomR(A, M) x HomR(B, M) b) HomR(M, A x B) is isomorphic to HomR(M, A) x HomR(M, B)
  14. I

    Stuck on the Final Module: 3 Questions Answered

    now this is my final module, i have three question a cannot answer click the link to get a pic of what i have done for this perticular question, I'm stuck at the last line i wrote. http://images.cardomain.com/member_images/5/web/557000-557999/557901_30_full.jpg another quetion asks a...
  15. C

    Calculate Speed and Time to Revolve Around the Moon

    if the command module is 60 miles above the surface of the moon it wants me to calculate the speed of the module adn the time it takes to complete one revolutionaround the mooon? givens mass moon = 7.35 * 10 to the 22 power radius moon = 1.74 * 10 to the 6 power altitude above the surface...
  16. wolram

    STIMON caused a protection fault in module user.exe

    i have a problem can somone help please, i have this message with a blue screen, STIMON caused a protection fault in module user.exe at 0003:00009e46 i have a printer and scanner connected anthon 1.8
  17. D

    Has Linux Kernel Module Support Improved in Recent Years?

    [SOLVED] Linux kernel module support How is it these days? IMO this is one of major areas where Linux used to lag behind Windows. Loading/unloading modules during runtime was not always reliable and sort of a pain... has it been improved in the last year or two?
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