Adequacy of nonsingular matrices over commutative principal ideal domains

Authors

  • V. Bovdi United Arab Emirates University, P.O. Box 15551, Al Ain, UAE
  • V. Shchedryk Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, 3-b Naukova str., 79060, Lviv, Ukraine https://orcid.org/0000-0003-4536-5276
https://doi.org/10.15330/cmp.18.1.236-249

Keywords:

adequate ring, principal ideal domain, divisor of a matrix
Published online: 2026-06-26

Abstract

The notion of adequacy for commutative domains was introduced by O. Helmer in [Bull. Amer. Math. Soc. 1943, 49 (4), 225-236]. In the present paper, we extend the concept of adequacy to noncommutative Bézout rings. We show that the set of nonsingular $2 \times 2$ matrices over a commutative principal ideal domain is adequate.

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How to Cite
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Bovdi, V.; Shchedryk, V. Adequacy of Nonsingular Matrices over Commutative Principal Ideal Domains. Carpathian Math. Publ. 2026, 18, 236-249.