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Algebra and Discrete Mathematics, 2014, Volume 17, Issue 1, Pages 1–11
(Mi adm455)
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This article is cited in 1 scientific paper (total in 1 paper)
RESEARCH ARTICLE
Rigid, quasi-rigid and matrix rings with $(\overline{\sigma},0)$-multiplication
Cihat Abdioĝlua, Serap Şahinkayab, Arda KÖRb a Department of Mathematics, Karamanoğlu Mehmetbey University, Yunus Emre Campus, Karaman, Turkey
b Department of Mathematics, Gebze Institute of Technology, Çayirova Campus, 41400 Gebze-Kocaeli, Turkey
Abstract:
Let $R$ be a ring with an endomorphism $\sigma$. We introduce $(\overline{\sigma}, 0)$-multiplication which is a generalization of the simple $ 0$-multiplication. It is proved that for arbitrary positive integers $m\leq n$ and $n\geq 2$, $R[x; \sigma]$ is a reduced ring if and only if $S_{n, m}(R)$ is a ring with $(\overline{\sigma},0)$-multiplication.
Keywords:
simple $0$-multiplication, quasi $\sigma$-rigid rings.
Received: 26.04.2012 Revised: 19.12.2012
Citation:
Cihat Abdioĝlu, Serap Şahinkaya, Arda KÖR, “Rigid, quasi-rigid and matrix rings with $(\overline{\sigma},0)$-multiplication”, Algebra Discrete Math., 17:1 (2014), 1–11
Linking options:
https://www.mathnet.ru/eng/adm455 https://www.mathnet.ru/eng/adm/v17/i1/p1
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Abstract page: | 234 | Full-text PDF : | 95 | References: | 44 |
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