Demonstrates adequacy of nonsingular matrices over commutative principal ideal domains, indicating an extension of existing concepts.
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 × 2 matrices over a commutative principal ideal domain is adequate.
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Bovdi et al. (2026) studied this question.
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