16 нояб. 2014 г. · The group ring R[G] is the ring of polynomials with coefficients in R and variables coming from G (which explains the notation). However, we ...

29 окт. 2013 г. · Let Q be the rationals and G a group. Then we consider the group ring Q[G].

28 июл. 2013 г. · If R is an integral domain (I am having Z or a field in mind) and G a (not necessarily finite) group then we can form the group ring R(G).

27 февр. 2018 г. · The main application of group rings is in representation theory of groups. They give a way of translating group theoretic problems into ...

6 мая 2016 г. · Let R be a nontrivial commmutative ring and G a group. Prove that R[G] is commutative if and only if G is abelian.

21 февр. 2018 г. · 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.

20 июл. 2010 г. · The main difference between groups and rings is that rings have two binary operations (usually called addition and multiplication) instead of just one binary ...

21 мая 2011 г. · What I can say is that as a coalgebra, a group Hopf algebra looks extremely simply: It is a direct sum of 1-dimensional coalgebras, each of ...

18 нояб. 2016 г. · Let R be a ring and G an infinite multiplicative cyclic group with generator g. Is the group ring R(G)≅R[x]?

3 окт. 2020 г. · Center of a group ring? ... Let R be a ring with unity and let G be a group. Then what is the center of the group ring R(G)? ... Hence x∈Z(R(G)). Is ...