SKEW POLYNOMIAL RINGS OVER SEMIPRIME RINGS

• Published in: Journal of the Korean Mathematical Society Vol. 47; no. 5; pp. 879 - 897
• Main Authors: Hong, Chan-Yong, Kim, Nam-Kyun, Lee, Yang
• Format: Journal Article
• Language: English
• Published: 대한수학회 01.09.2010
• Subjects: 수학
• ISSN: 0304-9914; 2234-3008
• DOI: 10.4134/JKMS.2010.47.5.879

Y. Hirano introduced the concept of a quasi-Armendariz ring which extends both Armendariz rings and semiprime rings. A ring R is called quasi-Armendariz if aiRbj = 0 for each i, j whenever polynomials [수식]. In this paper, we first extend the quasi-Armendariz property of semiprime rings to the skew polynomial rings, that is, we show that if R is a semiprime ring with an epimorphism δ, then [수식] for any integer k ≥ 0 and i, j, where [수식]Moreover, we extend this property to the skew monoid rings, the Ore extensions of several types, and skew power series ring, etc. Next we define δ-skew quasi-Armendariz rings for an endomorphism δ of a ring R. Then we study several extensions of δ-skew quasi-Armendariz rings which extend known results for quasi-Armendariz rings and δ-skew Armendariz rings. KCI Citation Count: 7