Dinesh Khurana

activity

20082024

most citedGroup Rings that are Additively Generated by Idempotents and Units

2 citations · 2 across the 7 of their papers we have counts for

collaborators

8 papers

math.RA2024

Ring Elements of Stable Range One

Dinesh Khurana, T. Y. Lam

A ring element $a \in R$ is said to be of {\it right stable range one\/} if, for any $t \in R$ , $a R + tR = R$ implies that $a + t b$ is a unit in $R$ for some $b \in R$ …

math.RA2023

A New Determinantal Formula for Three Matrices

Dinesh Khurana, T. Y. Lam

For any three $n \times n$ matrices $A, B, X$ over a commutative ring $S$ , we prove that $det (A + B - A X B) = det (A + B - B X A) \in S$ . This apparently new formula may…

math.RA2018

Commutators and Anti-Commutators of Idempotents in Rings

Dinesh Khurana, T. Y. Lam

We show that a ring $R$ has two idempotents $e, e^{'}$ with an invertible commutator $e e^{'} - e^{'} e$ if and only if $R ≅ M_{2} (S)$ for a ring $S$ in which $\,…

math.RA2015

Unit-Regularity of Regular Nilpotent Elements

Dinesh Khurana

Let $a$ be a regular element of a ring $R$ . If either $K := r_{R} (a)$ has the exchange property or every power of $a$ is regular, then we prove that for every positive integer $n$ …

math.RA2010

A quantum-trace determinantal formula for matrix commutators, and applications

Dinesh Khurana, T. Y. Lam, Noam Shomron

In this paper, we establish a determinantal formula for 2 x 2 matrix commutators [X,Y] = XY - YX over a commutative ring, using (among other invariants) the quantum traces of X and…

math.RA2009

A short proof of Grinshpon's theorem

Dinesh Khurana

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 $d e t (A)$ is invertible in $R$ . We give a very short proof…