pith. sign in

arxiv: 1806.04747 · v1 · pith:X5TXEISSnew · submitted 2018-06-12 · 🧮 math.RA · math.KT

Commutative Bezout domains of stable range 1.5

classification 🧮 math.RA math.KT
keywords rangestablecommutativebezoutcanonicalchosencommondivisor
0
0 comments X
read the original 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.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.