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

Sang Bok Nam, Sung Ju Ryu, Sang Jo Yun


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.

Subject classification

16S36, 16S50


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