Square-Free Rings And Their Automorphism Group
Rings and Algebras
2008-09-30 v1
Abstract
Finite-dimensional square-free algebras have been completely characterized by Anderson and D'Ambrosia as certain twisted semigroup algebras over a square-free semigroup S with coefficients in a field K. D'Ambrosia extended the definition of square-free to artinian rings with unity and showed every square-free ring has an associated division ring D and square-free semigroup S. We show a square-free ring can be characterized as a twisted semigroup ring over a square-free semigroup S with coefficients in a division ring D. Also, to each square-free ring there exists a short exact sequence connecting the outer automorphisms of a square-free ring to certain cohomology groups related to S and D.
Cite
@article{arxiv.0809.4878,
title = {Square-Free Rings And Their Automorphism Group},
author = {Martin W. Montgomery},
journal= {arXiv preprint arXiv:0809.4878},
year = {2008}
}
Comments
18 pages, 1 figure