Modules Definition and 224 Threads

I am reading Paul E. Bland's book "Rings and Their Modules" ... Currently I am focused on Section 4.2 Noetherian and Artinian Modules ... ... I need some help in order to fully understand Example 3, Section 4.2 ... Example 3, Section 4.2 reads as follows: My questions are as...

I am new on this forum, this is my gift for you. Suppose ##(M_i)_{i \in I}## is a family of left ##R##-modules and ##M = \bigoplus_{i \in I} M_i## (external direct sum). Suppose ##N = \langle x_1, \cdots ,x_m \rangle## is a finitely generated submodule of ##M##. Then for each ##j = 1, \cdots...

I am reading Paul E. Bland's book: Rings and Their Modules and am currently focused on Section 2.2 Free Modules ... ... I need someone to check my solution to the first part of Problem 1(a) of Problem Set 2.2 ... Problem 1(a) of Problem Set 2.2 reads as follows: My solution/proof of the...

Homework Statement I am reading Paul E. Bland's book: Rings and Their Modules and am currently focused on Section 2.2 Free Modules ... ... I need someone to check my solution to the first part of Problem 1(a) of Problem Set 2.2 ... Problem 1(a) of Problem Set 2.2 reads as follows: Can...

I am reading Paul E. Bland's book: Rings and Their Modules and am currently focused on Section 2.1 Direct Products and Direct Sums ... ... I need help with some aspects of the proof of Proposition 2.1.4 ... Proposition 2.1.4 and its proof read as follows: In the above proof by Paul Bland we...

I am reading Paul E. Bland's book: Rings and Their Modules and am currently focused on Section 2.1 Direct Products and Direct Sums ... ... I need help with some aspects of the proof of Proposition 2.1.4 ... Proposition 2.1.4 and its proof read as follows: In the above proof by Paul Bland we...

For those MHB members who are interested in the theory of rings and their modules at the advanced undergraduate and beginning graduate levels it is hard to go past the book by Paul E. Bland and the book by Berrick and Keating ... namely ... "Rings and Their Modules" by Paul E. Bland (De Gruyter...

I am reading Paul E. Bland's book: Rings and Their Modules and am currently focused on Section 2.1 Direct Products and Direct Sums ... ... I need help with another aspect of the proof of Proposition 2.1.1 ... Proposition 2.1.1 and its proof read as follows...

I am reading Paul E. Bland's book: Rings and Their Modules and am currently focused on Section 2.1 Direct Products and Direct Sums ... ... I need help with another aspect of the proof of Proposition 2.1.1 ... Proposition 2.1.1 and its proof read as follows:In the above proof by Paul Bland we...

I am reading Paul E. Bland's book: Rings and Their Modules and am currently focused on Section 2.1 Direct Products and Direct Sums ... ... I need help with some aspects of the proof of Proposition 2.1.1 ... Proposition 2.1.1 and its proof read as follows: In the statement of the above...

I am reading Paul E. Bland's book: Rings and Their Modules and am currently focused on Section 2.1 Direct Products and Direct Sums ... ... I need help with some aspects of the proof of Proposition 2.1.1 ... Proposition 2.1.1 and its proof read as follows: In the statement of the above...

I am reading P.M. Cohn's book: Introduction to Ring Theory (Springer Undergraduate Mathematics Series) ... ... I am currently focused on Section 2.2: Chain Conditions ... which deals with Artinian and Noetherian rings and modules ... ... I need help with understanding an aspect of the proof of...

I am reading P.M. Cohn's book: Introduction to Ring Theory (Springer Undergraduate Mathematics Series) ... ... I am currently focused on Section 2.2: Chain Conditions ... which deals with Artinian and Noetherian rings and modules ... ... I need help with understanding an aspect of the proof of...

I know that vector spaces have more structure as they are defined over fields and that modules are defined over rings. But it's hard to think of a situation where a using a ring clearly backfires. Is it just because a ring doesn't have an inverse for the second operation? For a module over Z...

Hi all, I study Mathematics and Theoretical Physics at university. Next year, I'll have a choice between three modules; Thermodynamics and Statistical Physics Cosmology Fluid Mechanics My main interest is Condensed Matter Physics; therefore, thermodynamics and statistical physics is a given...

I would like to read a book, the chapter of a book or a website article (preferably comprehensive) on the history of the concept of a module and the development of the theory of modules in mathematics ... Can anyone help with some good references ... Peter

Does anyone know of a book or web page that gives a history of the concept of a module and the history of modules in algebra ... i have not not been able to find a book that covers the history of modules nor a website ... Help will be appreciated... Peter

I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Section 6.1 The Jacobson Radical ... ... I need help with the proof of Proposition 6.1.7 ... Proposition 6.1.7 and its proof read as follows: In the above text from Bland, in the proof of (1), we read the...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Section 6.1 The Jacobson Radical ... ... I need help with the proof of Proposition 6.1.7 ... Proposition 6.1.7 and its proof read as follows: In the above text from Bland ... in the proof of (1) we read the...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Section 6.1 The Jacobson Radical ... ... I need help with the proof of Proposition 6.1.7 ...Proposition 6.1.7 and its proof read as follows: In the above text from Bland ... in the proof of (1) we read the...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Section 6.1 The Jacobson Radical ... ... I need help with the proof of Proposition 6.1.7 ... Proposition 6.1.7 and its proof read as follows:https://www.physicsforums.com/attachments/6388...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Section 6.1 The Jacobson Radical ... ... I need help with the proof of Proposition 6.1.7 ...Proposition 6.1.7 and its proof read as follows: In the above text from Bland, in the proof of (1) we read the following...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Chapter 1, Section 1.4 Modules ... ... I need help with the proving a statement Bland makes in Example 13 ... ... Example 13 reads as follows: In the above text from Bland, we read the following: " ... If ##N## is...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Chapter 1, Section 1.4 Modules ... ... I need help with the proving a statement Bland makes in Example 13 ... ... Example 13 reads as follows:In the above text from Bland, we read the following: " ... If N is a...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Section 6.1 The Jacobson Radical ... ... I need help with an aspect of Proposition 6.1.2 ... ... Proposition 6.1.2 relies on Zorn's Lemma and the notion of inductive sets ... ... so I am providing a short note...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Section 6.1 The Jacobson Radical ... ... I need help with an aspect of Proposition 6.1.2 ... ... Proposition 6.1.2 relies on Zorn's Lemma and the notion of inductive sets ... ... so I am providing a short note from...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Section 4.2: Noetherian and Artinian Modules and need some help to fully understand the proof of part of Proposition 4.2.4 ... ... Proposition 4.2.4 reads as follows: I need help to fully understand Part of the...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Section 4.2: Noetherian and Artinian Modules and need some help to fully understand the proof of part of Proposition 4.2.4 ... ... Proposition 4.2.4 reads as follows: I need help to fully understand Part of the...

I am reading J A Beachy's Book, Introductory Lectures on Rings and Modules"... ... I am currently focused on Chapter 2: Modules ... and in particular Section 2.4: Chain Conditions ... I need help with the proof of Proposition 2.4.5 ... Proposition 2.4.5 reads as follows: In the above text...

I am reading J A Beachy's Book, Introductory Lectures on Rings and Modules"... ... I am currently focused on Chapter 2: Modules ... and in particular Section 2.4: Chain Conditions ... I need help with the proof of Proposition 2.4.5 ...Proposition 2.4.5 reads as follows...

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 the proof of Lemma 1.2.21 ... Lemma 1.2.21 and its proof reads as follows: In the above text (in the proof) by Berrick and Keating we read the following:"... ...

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 the proof of Lemma 1.2.21 ... Lemma 1.2.21 and its proof reads as follows: Question 1In the above text by Berrick and Keating, we read the following:"... ... Since...

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 the proof of Lemma 1.2.21 ... Lemma 1.2.21 and its proof reads as follows: Question 1In the above text by Berrick and Keating, we read the following:"... ...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am trying to understand Section 4.1 on Generating and Cogenerating Classes ... ... In particular I am trying to understand and get a good sense of the notion of a module being finitely cogenerated ... Bland defines a finitely...

If the moderators agree, I have made a thread on the book of Bland - Rings and their Modules 2011.

I am reading Paul E. Bland's book "Rings and Their Modules ... Currently I am focused on Section 2.3 Tensor Products of Modules ... ... I need some help in order to fully understand the Remark that Bland makes on Pages 65- 66 Bland's remark reads as follows: Question 1 In the above text by...

I am reading Paul E. Bland's book "Rings and Their Modules ... Currently I am focused on Section 2.3 Tensor Products of Modules ... ... I need some help in order to fully understand the Remark that Bland makes on Pages 65- 66 Bland's remark reads as follows: Question 1 In the above text by...

I am reading Paul E. Bland's book "Rings and Their Modules ... Currently I am focused on Section 2.2 Free Modules ... ... I need some help in order to fully understand Bland's Example on page 56 concerning directly finite and directly infinite R-modules ... ... Bland's Example on page 56...

I am reading Paul E. Bland's book "Rings and Their Modules ... Currently I am focused on Section 2.2 Free Modules ... ... I need some help in order to fully understand the proof of the equivalence of (1) and (3) in Proposition 2.2.3 ... Proposition 2.2.3 and its proof reads as follows: Bland...

I am reading Paul E. Bland's book "Rings and Their Modules ... Currently I am focused on Section 2.2 Free Modules ... ... I need some help in order to fully understand the proof of the equivalence of (1) and (3) in Proposition 2.2.3 ... Proposition 2.2.3 and its proof reads as follows:Bland...

Hey! :o Let $R$ be a commutative ring with unit. I want to show that if each $R$-submodule of a free $R$-module is free then $R$ is P.I.D.. From the thread http://mathhelpboards.com/linear-abstract-algebra-14/how-can-we-conclude-i-principal-ideal-18593.html we have that if an ideal of $R$ is...

What limits the efficiency of a PV Module and a Thermal Collector? PV efficiecy is limited more by temperature in summer than by illumination in winter. Thermal Collector efficiency is limited by temperature and illumination in winter. The lower the temperature a thermal collector will be...

I am reading Donald S. Passmore's book "A Course in Ring Theory" ... I am currently focussed on Chapter 9 Tensor Products ... ... I need help in order to get a full understanding of the free abelian group involved in the construction of the tensor product ... ... The text by Passmore...

I've installed Python 3.5.1 successfully, and I've downloaded add-on modules such as numpy, scipy, matplotlib, etc, but when I try to import them into python I get the following: "ImportError: No module named 'numpy'", etc. There's no executable file in the numpy download to activate anything...

I am reading Dummit and Foote's book: Abstract Algebra ... ... and am currently focused on Section 10.4 Tensor Products of Modules ... ... I have a basic question regarding the extension of the scalars ... Dummit and Foote's exposition regarding extension of the scalars reads as...

What is the heat/cold ratio in thermoelectric modules to generate a specific voltage pls? old Bozo

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 Exercise 1.2.8 (c) ... Exercise 1.2.8 (c) reads as follows:Now ... from this exercise we have that M \equiv \mathbb{C}^3 ... and ... A = \begin{pmatrix} 0&1&1 \\...

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 in order to fully understand Example 1.2.2 (iv) [page 16] ... indeed, I am somewhat overwhelmed by this construction ... ... Example 1.2.2 (iv) reads as follows:My...

I am reading P.M. Cohn's book: Introduction to Ring Theory (Springer Undergraduate Mathematics Series) ... ... I am currently focused on Section 2.2: Chain Conditions ... which deals with Artinian and Noetherian rings and modules ... ... I need help to get started on Exercise 3, Section 2.2...

I am reading the book "An Introduction to Rings and Modules with K-theory in View" by A.J. Berrick and M.E. Keating ... ... I am currently focused on Chapter 3; Noetherian Rings and Polynomial Rings. I need someone to help me to fully understand the maximal condition for modules and its...