This article is cited in 2 papers

RESEARCH ARTICLE

Factorization of elements in noncommutative rings, I

Alberto Facchini^a, Martino Fassina<sup>b

a</sup> Dipartimento di Matematica, Universitá di Padova, 35121 Padova, Italy
^b Department of Mathematics, University of Illinois at Urbana-Champaign, 61801 Urbana, IL, USA

Abstract: We extend the classical theory of factorization in noncommutative integral domains to the more general classes of right saturated rings and right cyclically complete rings. Our attention is focused, in particular, on the factorizations of right regular elements into left irreducible elements. We study the connections among such factorizations, right similar elements, cyclically presented modules of Euler characteristic $0$ and their series of submodules. Finally, we consider factorizations as a product of idempotents.

Keywords: divisibility, factorization, right irreducible element.

MSC: 16U30, 16B99

Received: 11.01.2016
Revised: 09.02.2016

Language: English

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