1 citations · 3 across the 10 of their papers we have counts for
13 papers
Matrix invertible extensions over commutative rings. Part II: determinant liftability
Grigore Călugăreanu, Horia F. Pop, Adrian Vasiu
A unimodular matrix with entries in a commutative ring is called weakly determinant liftable if there exists a matrix congruent to modulo and…
Matrix invertible extensions over commutative rings. Part I: general theory
Grigore Călugăreanu, Horia F. Pop, Adrian Vasiu
A unimodular matrix with entries in a commutative is called extendable (resp.\ simply extendable) if it extends to an invertible matrix (resp.\ invertib…
On perspective Abelian groups
Grigore Calugareanu, Andrey Chekhlov
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 gr…
The -semiprimeness of Rings
Grigore Călugăreanu, Tsiu-Kwen Lee, Jerzy Matczuk
For a nonempty subset of a ring , the ring is called -semiprime if, given , implies . This provides a proper class of semiprime rings. First, we…
The formula ABA=Tr(AB)A for matrices
Grigore Calugareanu
We prove that this formula characterizes the square matrices over commutative rings for which all 2 x 2 minors equal zero.
On matrix invertible extensions over commutative rings
Grigore Calugareanu, Horia F. Pop, Adrian Vasiu
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. inve…