Rings and Their Modules .... ....

In summary: Keep up the great work!In summary, for those interested in the theory of rings and their modules at the advanced undergraduate and beginning graduate levels, there are several useful books available. These include "Rings and Their Modules" by Paul E. Bland, "An Introduction to Rings and Modules" by A.J. Berrick and M.E. Keating, "Rings and Categories of Modules" by Frank W. Anderson and Kent R. Fuller, and "Foundations of Commutative Rings and Their Modules" by Fanggui Wang and Hwankoo Kim. Having multiple sources can be helpful in understanding a difficult topic, and the different perspectives offered by these texts may be beneficial. Members of the MHB community are encouraged to
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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 2011) [452 pages]

"An Introduction to Rings and Modules: With K-Theory in View" by A.J. Berrick and M.E. Keating (Cambridge University Press, 2000) [265 pages]

It is helpful, however, when finding a topic difficult, to have some alternate sources of theory development and presentation ... and two books I have come across are useful in that (if a bit challenging). One is an older book and the other is comparatively hot off the press from China ... details of the books are as follows:

"Rings and Categories of Modules" (Second Edition) by Frank W. Anderson and Kent R. Fuller (Springer-Verlag 1992) [376 pages]

"Foundations of Commutative Rings and Their Modules" by Fanggui Wang and Hwankoo Kim (Springer 2016) [699 pages]Members interested in ring and module theory may wish to check these books out on Amazon or other web sites ...

Peter
 
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, thank you for sharing these resources with the MHB community! I have not personally read these books, but as a fellow scientist, I can appreciate the value of having multiple sources for learning and understanding a complex topic. It's always helpful to have different perspectives and approaches to a subject, especially when it comes to advanced topics like ring and module theory.

I am particularly intrigued by the book "Foundations of Commutative Rings and Their Modules" by Wang and Kim. It's always interesting to see how different countries and cultures approach mathematical concepts, and I think it will be exciting to see how the Chinese perspective is reflected in this text.

I hope that other MHB members interested in ring and module theory will take advantage of these resources and continue to expand their knowledge and understanding of this fascinating subject. Thank you again for sharing!
 

Related to Rings and Their Modules .... ....

1. What is a ring and its modules?

A ring is an algebraic structure that consists of a set of elements with two binary operations: addition and multiplication. A module over a ring is an algebraic structure that generalizes the notion of vector spaces over a field, where the scalars come from the ring instead of a field.

2. What are the properties of a ring and its modules?

A ring must satisfy the following properties: closure under addition and multiplication, associativity and commutativity of addition and multiplication, existence of an additive identity and a multiplicative identity, and the distributive property. Modules must satisfy the properties of a ring as well as the distributive property of scalar multiplication.

3. What is the difference between a ring and a field?

A ring is a generalization of a field, with the main difference being that a field has multiplicative inverses for all non-zero elements, while a ring may not have multiplicative inverses for all elements. In other words, every field is a ring, but not every ring is a field.

4. How are rings and modules used in mathematics and other fields?

Rings and modules are used in various areas of mathematics, including abstract algebra and number theory. They also have applications in fields such as physics and computer science, particularly in areas involving linear algebra and group theory.

5. Can rings and modules be applied to real-world problems?

Yes, rings and modules have practical applications in fields such as coding theory, cryptography, and signal processing. They can also be used to model and solve real-world problems in various industries, such as finance and engineering.

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