Finite homomorphic images of Bezout duo-domains

Authors

  • O.S. Sorokin Ivan Franko Lviv National University, 1 Universytetska str., 79000, Lviv, Ukraine
https://doi.org/10.15330/cmp.6.2.360-366

Keywords:

Bezout ring, duo-domain, distributive ring, stable range 1, square-free element, adequate element, von Neumann regular ring, morphic ring, weak global dimension
Published online: 2014-12-29

Abstract

It is proved that for a quasi-duo Bezout ring of stable range 1 the duo-ring condition is equivalent to being an elementary divisor ring. As an application of this result a couple of useful properties are obtained for finite homomorphic images of Bezout duo-domains: they are coherent morphic rings, all injective modules over them are flat, their weak global dimension is either 0 or infinity. Moreover, we introduce the notion of square-free element in noncommutative case and it is shown that they are adequate elements of Bezout duo-domains. In addition, we are going to prove that these elements are elements of almost stable range 1, as well as necessary and sufficient conditions for being square-free element are found in terms of regularity, Jacobson semisimplicity, and boundness of weak global dimension of finite homomorphic images of Bezout duo-domains.

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How to Cite
(1)
Sorokin, O. Finite Homomorphic Images of Bezout Duo-Domains. Carpathian Math. Publ. 2014, 6, 360-366.