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We prove that a commutative Bezout ring is an Hermitian ring if and only if it is a Bezout ring of stable rank 2. It is shown that a noncommutative Bezout ring of stable rank 1 is an Hermitian ring. This implies that a noncommutative semilocal Bezout ring is an Hermitian ring. We prove that the Bezout domain of stable rank 1 with two-element group of units is a ring of elementary divisors if and only if it is a duo-domain. 相似文献
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We investigate Bezout domains in which an arbitrary maximally-nonprincipal right ideal is two-sided. In the case of At(R) Bezout domains, we show that an arbitrary maximally-nonprincipal two-sided right ideal is also a maximally-nonprincipal left ideal. 相似文献
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