Blogs about: Group Ring
Featured Blog
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 generating set ). Define by and . Use this to make into an -module and compute the exterior power over .… more →
Project Crazy Project
Compute an exterior power
wrote 1 year ago: 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
wrote 2 years ago: 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
wrote 2 years ago: 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
wrote 2 years ago: 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
wrote 2 years ago: 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
wrote 2 years ago: 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
wrote 2 years ago: Consider the following elements of the group ring : and . Compute , , , , and . Evidently, … more →
Compute in a group ring
— 2 comments
wrote 2 years ago: Consider the following elements of the integral group ring : and . Compute the following elements: , … more →
Compute in a group ring over Dih(8)
wrote 2 years ago: Let and be elements of the group ring . Compute the following: , , , and . Evidently, … more →
The group ring isomorphism problem (1)
wrote 2 years ago: 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
wrote 3 years ago: Let’s define a new concept that seems to be really important in algebraic number theory, that … more →
A-W Consequences
— 1 comment
wrote 3 years ago: I said I’d do the uniqueness part of Artin-Wedderburn, but I’ve decided not to prove it. … more →
Irreducible iff simple
wrote 3 years ago: 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
wrote 3 years ago: As usual, ordering of presenting this material and level of generality are proving to be difficult d … more →
Representation Theory III
— 2 comments
wrote 3 years ago: 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
wrote 3 years ago: I know everyone and their brother does a series of posts on basic representation theory, and I said … more →
