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arXiv · 1806.04747

Commutative Bezout domains of stable range 1.5

Victor A. Bovdi·Volodymyr P. Shchedryk
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Abstract

A ring R is said to be of stable range 1.5 if for each a, b from R and nonzero c from R satisfying aR + bR + cR = R there exists r from R such that (a + br)R + cR = R. Let R be a commutative domain in which all finitely generated ideals are principal, and let R be of stable range 1.5. Then each matrix A over R is reduced to Smith's canonical form by transformations PAQ in which P and Q are invertible and at least one of them can be chosen to be a product of elementary matrices. We generalize Helmer's theorem about the greatest common divisor of entries of A over R.

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Victor A. Bovdi, Volodymyr P. Shchedryk. 2018-06-12. Commutative Bezout domains of stable range 1.5. https://arxiv.org/abs/1806.04747

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