SKEW POLYNOMIAL RINGS OVER SEMIPRIME RINGS Hong, Chan-Yong; Kim, Nam-Kyun; Lee, Yang;
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 = 0 for each i, j whenever polynomials , satisfy f(x)R[x]g(x) = 0. 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 , then f(x)R[x; ]g(x) = 0 implies for any integer k 0 and i, j, where , . 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 -skew quasi-Armendariz rings for an endomorphism of a ring R. Then we study several extensions of -skew quasi-Armendariz rings which extend known results for quasi-Armendariz rings and -skew Armendariz rings.