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2 results on '"KHURANA, DINESH"'

1. Group Rings that are Additively Generated by Idempotents and Units

Author

Khurana, Dinesh and Kumar, Chanchal

Subjects
Mathematics::Commutative Algebra, Rings and Algebras (math.RA), FOS: Mathematics, Mathematics - Rings and Algebras
Abstract

We study clean group rings and also the group rings whose every element is a sum of two units. We also prove that if R is an Abelian exchange ring and G is a locally finite group, then the group ring RG has stable range one., 5 pages

Published
2009

2. A short proof of Grinshpon's theorem

Author

Khurana, Dinesh

Subjects
Mathematics::Commutative Algebra, Mathematics::Operator Algebras, Rings and Algebras (math.RA), Mathematics::Rings and Algebras, FOS: Mathematics, Mathematics - Rings and Algebras
Abstract

Grinshpon has proved that if $S$ is a commutative subring of a ring $R$ and $A\in M_n(S)$ is invertible in $M_n(R)$, then $det(A)$ is invertible in $R$. We give a very short proof of the result., Comment: 1 page

Published
2009
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