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arXiv · 0809.4878

Square-Free Rings And Their Automorphism Group

Martin W. Montgomery
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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.

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Martin W. Montgomery. 2008-09-29. Square-Free Rings And Their Automorphism Group. https://arxiv.org/abs/0809.4878

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