The group ring R[G] R [G] is the ring of polynomials with coefficients in R R and variables coming from G G (which explains the notation). However, we define the multiplication of two polynomials using the …

Feb 21, 2018 · A group ring $R [G]$ is the set of linear combinations of elements of the group, with coefficients in the ring, endowed with the natural operations (notably the product in $R [G]$ …

Apr 29, 2017 · The group ring Z[G], on the other hand, knows at least as much as k[G] for every k (which one can obtain by tensoring with k); this information should let you deduce something about the …

Rings, groups, and fields all feel similar. What are the differences between them, both in definition and in how they are used?

Oct 29, 2013 · Explore related questions ring-theory group-rings See similar questions with these tags.

May 23, 2021 · A ring is a set that forms an abelian group with respect to one operation and follow some other properties with another Operation if we are able to define. Concluding, All rings are abelian …

Jan 11, 2017 · A ring is an abelian group (under addition, say) that happens to have a second closed, associative, binary operation as well. And these two operations satisfy a distribution law.

Jul 21, 2025 · It is known that a group ring R[G] R [G] is a unique factorization domain (UFD) if and only if R R is a UFD and G G is a torsion-free abelian group. Question: Has there been any study into the …

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 …

Oct 13, 2023 · 0 Here is the question I am trying to understand its solution: Give an example of a zero divisor in the group ring Z(C3) Z (C 3) where C3 C 3 is the cyclic group with 3 elements. My …