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Algebra and Discrete Mathematics, 2016, Volume 22, Issue 2, Pages 209–232
(Mi adm584)
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This article is cited in 2 scientific papers (total in 2 papers)
RESEARCH ARTICLE
Factorization of elements in noncommutative rings, I
Alberto Facchinia, Martino Fassinab a 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.
Received: 11.01.2016 Revised: 09.02.2016
Citation:
Alberto Facchini, Martino Fassina, “Factorization of elements in noncommutative rings, I”, Algebra Discrete Math., 22:2 (2016), 209–232
Linking options:
https://www.mathnet.ru/eng/adm584 https://www.mathnet.ru/eng/adm/v22/i2/p209
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Abstract page: | 326 | Full-text PDF : | 110 | References: | 35 |
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