Diagonal reduction of matrices over commutative semihereditary Bezout rings
نویسندگان
چکیده
منابع مشابه
Diagonal Matrix Reduction over Refinement Rings
Abstract: A ring R is called a refinement ring if the monoid of finitely generated projective R- modules is refinement. Let R be a commutative refinement ring and M, N, be two finitely generated projective R-nodules, then M~N if and only if Mm ~Nm for all maximal ideal m of R. A rectangular matrix A over R admits diagonal reduction if there exit invertible matrices p and Q such that PAQ is...
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The class of Bézout factorial rings is introduced and characterized. Using the factorial properties of such a ring R, and given a n×m matrix A over R, we find P ∈ GL(n, R) and Q ∈ GL(m, R) such that PAQ is diagonal with every element in the diagonal dividing the following one. Key-words: Ring, Bézout, principal, factorization, reduction of matrices.
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We prove that each almost local-global semihereditary ring R has the stacked bases property and is almost Bézout. More precisely, if M is a finitely presented module, its torsion part tM is a direct sum of cyclic modules where the family of annihilators is an ascending chain of invertible ideals. These ideals are invariants of M. Moreover M/tM is a projective module which is isomorphic to a dir...
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We prove that each almost local-global semihereditary ring R has the stacked bases property and is almost Bézout. More precisely, if M is a finitely presented module, its torsion part tM is a direct sum of cyclic modules where the family of annihilators is an ascending chain of invertible ideals. These ideals are invariants of M . Moreover M/tM is a projective module which is isomorphic to a di...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2019
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927872.2018.1521419