SKEW POLYNOMIAL RINGS OVER SEMIPRIME RINGS

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 p...

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Published inJournal 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
LanguageEnglish
Published 대한수학회 01.09.2010
Subjects
수학
Online AccessGet full text
ISSN0304-9914
2234-3008
DOI10.4134/JKMS.2010.47.5.879

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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 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
AbstractList 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
Author Hong, Chan-Yong
Kim, Nam-Kyun
Lee, Yang
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CitedBy_id crossref_primary_10_1142_S0219498816500869
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crossref_primary_10_4134_CKMS_2011_26_4_557
crossref_primary_10_1017_S001708951500021X
crossref_primary_10_4134_JKMS_2015_52_6_1161
Cites_doi 10.1007/s10468-005-0707-y
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10.1016/j.jpaa.2007.01.018
10.1081/AGB-200053826
10.1017/S0017089509990243
10.1080/00927879808826274
10.1006/jabr.1999.8017
10.1016/S0022-4049(01)00053-6
10.1081/AGB-200034148
10.1081/AGB-120013179
10.1080/00927877708822194
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Title SKEW POLYNOMIAL RINGS OVER SEMIPRIME RINGS
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