• Korean Journal of Mathematics
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• v.21 no.4
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• pp.421-428
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• 2013

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 ${\alpha}$-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.