Adequacy of nonsingular matrices over commutative principal ideal domains

Abstract: The notion of the adequacy of commutative domains was introduced by Helmer in Bull. Amer.Math. Soc., 49 (1943), 225--236. In the present paper we extend the concept of adequacy to noncommutative B\'ezout rings. We show that the set of nonsingular second-order matrices over a commutative principal ideal domain is adequate.