Korean J. Math. Vol. 21 No. 4 (2013) pp.421-428
DOI: https://doi.org/10.11568/kjm.2013.21.4.421

On coefficients of nilpotent polynomials in skew polynomial rings

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Published: Dec 4, 2013
Mathematics Subject Classification:
16S36, 16S50

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Sang Bok Nam
Kyungdong University
Sung Ju Ryu
Pusan National University
Sang Jo Yun

Abstract

We observe the basic structure of the products of coefficients of nilpotent (left) polynomials in skew polynomial rings. This study consists of a process to extend a well-known result for semi-Armendariz rings. We introduce the concept of {\it $\alpha$-skew $n$-semi-Armendariz ring}, where $\alpha$ is a ring endomorphism. We prove that a ring $R$ is $\alpha$-rigid if and only if the $n$ by $n$ upper triangular matrix ring over $R$ is $\bar\alpha$-skew $n$-semi-Armendariz. This result are applicable to several known results.


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