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SKEW POLYNOMIAL RINGS OVER SEMIPRIME RINGS
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 Title & Authors
SKEW POLYNOMIAL RINGS OVER SEMIPRIME RINGS
Hong, Chan-Yong; Kim, Nam-Kyun; Lee, Yang;
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 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 = 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.
 Keywords
semiprime ring;quasi-Armendariz ring;skew polynomial ring;
 Language
English
 Cited by
1.
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2.
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대한수학회지, 2015. vol.52. 6, pp.1161-1178 crossref(new window)
1.
Annihilator Ideals of Noncommutative Ring Constructions, Communications in Algebra, 2016, 44, 1, 63  crossref(new windwow)
2.
Quasi-Armendariz generalized power series rings, Journal of Algebra and Its Applications, 2016, 15, 05, 1650086  crossref(new windwow)
3.
QUASI-ARMENDARIZ PROPERTY FOR SKEW POLYNOMIAL RINGS, Communications of the Korean Mathematical Society, 2011, 26, 4, 557  crossref(new windwow)
4.
GENERALISED ARMENDARIZ PROPERTIES OF CROSSED PRODUCT TYPE, Glasgow Mathematical Journal, 2016, 58, 02, 313  crossref(new windwow)
5.
INSERTION-OF-FACTORS-PROPERTY ON SKEW POLYNOMIAL RINGS, Journal of the Korean Mathematical Society, 2015, 52, 6, 1161  crossref(new windwow)
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Special properties of the ring Sn(R), Journal of Algebra and Its Applications, 2016, 1750212  crossref(new windwow)
7.
The Some Properties of Skew Polynomial Rings, Advances in Pure Mathematics, 2016, 06, 07, 507  crossref(new windwow)
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