Apr 29, 2017 · You might consult Chapter 9 in Milies, Sehgal, "An Introduction to Group Rings". It discusses how several invariants of groups are encoded in their integral group rings, and how this leads to an affirmative answer of the integral group ring isomorphism problem for …

I'll try again. First question: what's the meaning of the expression RG-module (I've found it in Robinson textbook)? Does it stand for the module over the group ring RG (R ring, G group)? Question 2: can the group ring RG have the structure of a module? $\endgroup$ –

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A ring is an abelian group with an additional operation, where the second operation is associative and the distributive property make the two operations "compatible". A field is a ring such that the second operation also satisfies all the properties of an abelian group (after throwing out the additive identity), i.e. it has multiplicative ...

Two good resources I can recommend are Passman's Algebraic structure of group rings and Lam's First course on noncommutative rings I think has some information on this. I don't have copies of Milies' group ring books, but I remember when I …

Sep 2, 2019 · How to recover the integral group ring? 2. What does this linear system look like? 3.

The algebraic structure of group rings. Pure and Applied Mathematics. Pure and Applied Mathematics. Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1977.

May 8, 2021 · If A is a ring, we say that A is semisimple if the free A-module of rank 1 is completely reducible. The version of Maschke's Theorem in the notes states: Let G be a finite group and suppose that $|G| \not= 0$ in the field k. Let U be a G-stable subspace of a finite-dimensional G-representation V.

Oct 3, 2020 · Center of a ring is a subring that contains identity, but what happens in the case of ring of all Even integers? 1 Surjective Ring Homomorphism mapping center to center

$\begingroup$ In response to your last paragraph, I learned that one way to think about Hopf algebras in general is to think of them as those algebras whose representations behave like the representations of a finite group in certain ways.