A. Vasiu

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20242026

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math.AC2025

Matrix invertible extensions over commutative rings. Part III: Hermite rings

Grigore CÄlugÄreanu, Horia F. Pop, Adrian Vasiu

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 \tex…

math.AC2025

Matrix invertible extensions over commutative rings. Part II: determinant liftability

Grigore CÄlugÄreanu, Horia F. Pop, Adrian Vasiu

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…

math.AC2024

Matrix invertible extensions over commutative rings. Part I: general theory

Grigore CÄlugÄreanu, Horia F. Pop, Adrian Vasiu

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.\ invertib…