The concept of the quasi-Armendariz property of rings properly contains Armendariz rings and semiprime rings. In this paper, we extend the quasi-Armendariz property for a polynomial ring to the skew polynomial ring, hence we call such ring a σ-quasi-Armendariz ring for a ring endomorphism σ, and investigate its structures, several extensions and related properties. In particular, we study the semiprimeness and the quasi-Armendariz property between a ring R and the skew polynomial ring R[x; σ] of R, and so these provide us with an opportunity to study quasi-Armendariz rings and semiprime rings in a general setting, and several known results follow as consequences of our results. © 2011 The Korean Mathematical Society.
CITATION STYLE
Başer, M., & Kwak, T. K. (2011). Quasi-Armendariz property for skew polynomial rings. Communications of the Korean Mathematical Society, 26(4), 557–573. https://doi.org/10.4134/CKMS.2011.26.4.557
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