SKEW POLYNOMIAL RINGS OVER SEMIPRIME RINGS
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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.
Abstract
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.
참고문헌 (18)
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