Zobrazeno 1 - 10
of 355
pro vyhledávání: '"Calugareanu A"'
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
Autor:
Calugareanu, Grigore, Chekhlov, Andrey
As a special case of perspective R-modules, an Abelian goup is called perspective if isomorphic summands have a common complement. In this paper we describe many classes of such groups.
Externí odkaz:
http://arxiv.org/abs/2403.18434
For a nonempty subset $X$ of a ring $R$, the ring $R$ is called $X$-semiprime if, given $a\in R$, $aXa=0$ implies $a=0$. This provides a proper class of semiprime rings. First, we clarify the relationship between idempotent semiprime and unit-semipri
Externí odkaz:
http://arxiv.org/abs/2402.19374
Autor:
Cǎlugǎreanu, Grigore
Publikováno v:
Carpathian Journal of Mathematics, 2024 Jan 01. 40(1), 25-36.
Externí odkaz:
https://www.jstor.org/stable/27259294
Autor:
Calugareanu, Grigore
We prove that this formula characterizes the square matrices over commutative rings for which all 2 x 2 minors equal zero.
Externí odkaz:
http://arxiv.org/abs/2306.00801
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
Publikováno v:
In Journal of Pure and Applied Algebra January 2025 229(1)
Autor:
Calugareanu, Grigore
Let T be an n by n zero-square matrix over a commutative unital ring R. We show that T is similar to a multiple of E_1n if R is a GCD domain and n = 2, if R is a GCD domain with 2 not zero divisor and n = 3, but there are matrices which are not simil
Externí odkaz:
http://arxiv.org/abs/2108.12882