Geodesic
Rigid, quasi-rigid and matrix rings with $(\overline{\sigma},0)$-multiplication
Algebra and discrete mathematics, Tome 17 (2014) no. 1, pp. 1-11.

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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: quasi $\sigma$-rigid rings.
Mots-clés : simple $0$-multiplication 
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Cihat Abdioĝlu; Serap Şahinkaya; Arda KÖR. Rigid, quasi-rigid and matrix rings with $(\overline{\sigma},0)$-multiplication. Algebra and discrete mathematics, Tome 17 (2014) no. 1, pp. 1-11. http://geodesic.mathdoc.fr/item/ADM_2014_17_1_a0/

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