3 papers
math.NT2026
On the factorizations of integers via division algorithms for polynomials
Guram Donadze, Adrian Vasiu
We introduce and study several conditions related to the factorization problem of composite numbers. For this purpose, we employ cyclotomic polynomials, Sylvester resultants, and t…
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 matrix with entries in a commutative ring is called weakly determinant liftable if there exists a matrix congruent to modulo and…