Square-Free Rings And Their Automorphism Group

Details Square-Free Rings And Their Automorphism Group Square-Free Rings And Their Automorphism Group

2008-09-29

arxiv.org/abs/0809.4878v1

Mathematics

Rings and Algebras

18 pages, 1 figure

Scientific paper

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.

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