Zobrazeno 1 - 10
of 124
pro vyhledávání: '"POP, Horia"'
We reobtain and often refine prior criteria due to Kaplansky, McGovern, Roitman, Shchedryk, Wiegand, and Zabavsky--Bilavska and obtain new criteria for a Hermite ring to be an \textsl{EDR}. We mention three criteria: (1) a Hermite ring $R$ is an \tex
Externí odkaz:
http://arxiv.org/abs/2405.01234
A unimodular $2\times 2$ matrix $A$ with entries in a commutative ring $R$ is called weakly determinant liftable if there exists a matrix $B$ congruent to $A$ modulo $R\det(A)$ and $\det(B)=0$; if we can choose $B$ to be unimodular, then $A$ is calle
Externí odkaz:
http://arxiv.org/abs/2404.17656
A unimodular $2\times 2$ matrix with entries in a commutative $R$ is called extendable (resp.\ simply extendable) if it extends to an invertible $3\times 3$ matrix (resp.\ invertible $3\times 3$ matrix whose $(3,3)$ entry is $0$). We obtain necessary
Externí odkaz:
http://arxiv.org/abs/2404.05780
We introduce the class E2 (resp. SE2) of commutative rings R with the property that each unimodular 2 x 2 matrix with entries in R extends to an invertible 3 x 3 matrix (resp. invertible 3 x 3 matrix whose (3, 3) entry is 0). Among noetherian domains
Externí odkaz:
http://arxiv.org/abs/2303.08413
Autor:
Călugăreanu Grigore, Pop Horia F.
Publikováno v:
Special Matrices, Vol 12, Iss 1, Pp 47-55 (2024)
Over any GCD (greatest common divisor) commutative domain we show that the nontrivial 2×22\times 2 idempotent matrices are products of two nilpotent matrices. In order to find explicitly such decompositions, two procedures are described. Assisted by
Externí odkaz:
https://doaj.org/article/bad617155cb54886af452e96a6e5a2f9
Publikováno v:
In Journal of Pure and Applied Algebra January 2025 229(1)
Autor:
Calugareanu, Grigore, Pop, Horia F.
We characterize the idempotent stable range one $2\times 2$ matrices over commutative rings and in particular, the integral matrices with this property. Several special cases and examples complete the subject.
Externí odkaz:
http://arxiv.org/abs/2103.08944
Autor:
Calugareanu, Grigore, Pop, Horia F.
For 2 by 2 matrices over commutative rings, we prove a characterization theorem for left stable range 1 elements, we show that the stable range 1 property is left-right symmetric (also) at element level, we show that all matrices with one zero row (o
Externí odkaz:
http://arxiv.org/abs/2012.13909
Akademický článek
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Publikováno v:
In Intelligent Systems with Applications November 2022 16