Compute an exterior power

: Let be the group ring over the group of order 2. Let be a free -module of free rank 2 (and free gene … more →

Prove that the augmentation ideal of a given group ring is nilpotent

: Let be a prime and let be a finite -group. Prove that the augmentation ideal in the group ring is a … more →

Compute the nilradical of a given group ring

: Let be a ring with . Let be a prime and let be an abelian group of order . Prove that the nilradical … more →

Find a generating set for the augmentation ideal of a group ring

: Let be a commutative ring with and a finite group. Prove that the augmentation ideal in the group ri … more →

Characterize the center of a group ring — 2 comments

: Let be a conjugacy class in the finite group . Let be a ring with 1. Prove that the element is in th … more →

Exhibit an element in the center of a group ring — 5 comments

: Let be a ring with , and let be a finite group. Prove that the element is in the center of the group … more →

Compute in a group ring

: Consider the following elements of the group ring : and . Compute , , , , and . Evidently, … more →

Compute in a group ring — 2 comments

: Consider the following elements of the integral group ring : and . Compute the following elements: , … more →

Compute in a group ring over Dih(8)

: Let and be elements of the group ring . Compute the following: , , , and . Evidently, … more →

The group ring isomorphism problem (1)

: Let be a field or and two groups. It is clear that if then as algebras. The group ring isomorphism p … more →

Class sums — 1 comment

: Let’s define a new concept that seems to be really important in algebraic number theory, that … more →

A-W Consequences — 1 comment

: I said I’d do the uniqueness part of Artin-Wedderburn, but I’ve decided not to prove it. … more →

Irreducible iff simple

: Let’s try to be explicit about this, since I feel like I may keep beating around the bush. The … more →

Maschke and Schur — 1 comment

: As usual, ordering of presenting this material and level of generality are proving to be difficult d … more →

Representation Theory III — 2 comments

: Let’s set up some notation first. Recall that if is a representation, then it makes V into a k … more →

Representation Theory I — 5 comments

: I know everyone and their brother does a series of posts on basic representation theory, and I said … more →

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