Zobrazeno 1 - 10
of 133
pro vyhledávání: '"KHURANA, DINESH"'
Autor:
Khurana, Dinesh, Lam, T. Y.
A ring element $\,a\in R\,$ is said to be of {\it right stable range one\/} if, for any $\,t\in R$, $\,aR+tR=R\,$ implies that $\,a+t\,b\,$ is a unit in $\,R\,$ for some $\,b\in R$. Similarly, $\,a\in R\,$ is said to be of {\it left stable range one\
Externí odkaz:
http://arxiv.org/abs/2404.13251
Autor:
Khurana, Dinesh, Lam, T. Y.
For any three $\,n\times n\,$ matrices $\,A,B,X\,$ over a commutative ring $\,S$, we prove that $\,{\rm det}\,(A+B-AXB)={\rm det}\,(A+B-BXA) \in S$. This apparently new formula may be regarded as a ``ternary generalization'' of Sylvester's classical
Externí odkaz:
http://arxiv.org/abs/2308.04411
Publikováno v:
In Journal of Pure and Applied Algebra December 2023 227(12)
Autor:
Khurana, Dinesh, Nielsen, Pace P.
Publikováno v:
In Journal of Pure and Applied Algebra November 2023 227(11)
Autor:
Khurana, Dinesh, Lam, T. Y.
Publikováno v:
AMS Contemporary Mathematics Volume 715, 2018, 205-224
We show that a ring $\,R\,$ has two idempotents $\,e,e'\,$ with an invertible commutator $\,ee'-e'e\,$ if and only if $\,R \cong {\mathbb M}_2(S)\,$ for a ring $\,S\,$ in which $\,1\,$ is a sum of two units. In this case, the "anti-commutator" $\,ee'
Externí odkaz:
http://arxiv.org/abs/1808.02308
Autor:
Khurana, Dinesh
Let $a$ be a regular element of a ring $R$. If either $K:=\rm{r}_R(a)$ has the exchange property or every power of $a$ is regular, then we prove that for every positive integer $n$ there exist decompositions $$ R_R = K \oplus X_n \oplus Y_n = E_n \op
Externí odkaz:
http://arxiv.org/abs/1509.07944
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 Y. Special forms of this determinantal formula include a "trace versi
Externí odkaz:
http://arxiv.org/abs/1003.5420
Autor:
Khurana, Dinesh
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
Comment: 1 page
Externí odkaz:
http://arxiv.org/abs/0904.0906
Autor:
Khurana, Dinesh, Kumar, Chanchal
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.
Comment: 5 pages
Comment: 5 pages
Externí odkaz:
http://arxiv.org/abs/0904.0861