This paper mainly studies some properties of skew polynomial ring related to Morita invariance, Armendariz and (quasi)-Baer. First, we show that skew polynomial ring has no Morita invariance by the counterexample. The...This paper mainly studies some properties of skew polynomial ring related to Morita invariance, Armendariz and (quasi)-Baer. First, we show that skew polynomial ring has no Morita invariance by the counterexample. Then we prove a necessary condition that skew polynomial ring constitutes Armendariz ring. We lastly investigate that condition of skew polynomial ring is a (quasi)-Baer ring, and verify that the conditions is necessary, but not sufficient by example and counterexample.展开更多
In this paper we continue the study of various ring theoretic properties of Morita contexts.Necessary and sufficient conditions are obtained for a general Morita context or a trivial Morita context or a formal triangu...In this paper we continue the study of various ring theoretic properties of Morita contexts.Necessary and sufficient conditions are obtained for a general Morita context or a trivial Morita context or a formal triangular matrix ring to satisfy a certain ring property which is among being Kasch,completely primary,quasi-duo,2-primal,NI,semiprimitive,projective-free,etc.We also characterize when a general Morita context is weakly principally quasi-Baer or strongly right mininjective.展开更多
In this paper,we give the equivalent characterizations of principally quasi-Baer modules,and show that any direct summand of a principally quasi-Baer module inherits the property and any finite direct sum of mutually ...In this paper,we give the equivalent characterizations of principally quasi-Baer modules,and show that any direct summand of a principally quasi-Baer module inherits the property and any finite direct sum of mutually subisomorphic principally quasi-Baer modules is also principally quasi-Baer.Moreover,we prove that left principally quasi-Baer rings have Morita invariant property.Connections between Richart modules and principally quasi-Baer modules are investigated.展开更多
In this paper, the (quasi-)Baerness of skew group ring and fixed ring is investigated. The following two results are obtained: if R is a simple ring with identity and G an outer automorphism group, then R G is a Baer ...In this paper, the (quasi-)Baerness of skew group ring and fixed ring is investigated. The following two results are obtained: if R is a simple ring with identity and G an outer automorphism group, then R G is a Baer ring;if R is an Artinian simple ring with identity and G an outer automorphism group, then RG is a Baer ring. Moreover, by decomposing Morita Context ring and Morita Context Theory, we provided several conditions of Morita Context ring, which is formed of skew group ring and fixed ring, to be (quasi-)Baer ring.展开更多
Let R be a ring. We consider left （or right） principal quasi-Baerness of the left skew formal power series ring R[[x;α]] over R where a is a ring automorphism of R. We give a necessary and sufficient condition unde...Let R be a ring. We consider left （or right） principal quasi-Baerness of the left skew formal power series ring R[[x;α]] over R where a is a ring automorphism of R. We give a necessary and sufficient condition under which the ring R[[x; α]] is left （or right） principally quasi-Baer. As an application we show that R[[x]] is left principally quasi-Baer if and only if R is left principally quasi- Baer and the left annihilator of the left ideal generated by any countable family of idempotents in R is generated by an idempotent.展开更多
A generalization of semiprime rings and right p.q.-Baer rings,which we call quasi-Armendariz rings of differential inverse power series type(or simply,DTPS-quasi-Armendariz),is introduced and studied.It is shown that ...A generalization of semiprime rings and right p.q.-Baer rings,which we call quasi-Armendariz rings of differential inverse power series type(or simply,DTPS-quasi-Armendariz),is introduced and studied.It is shown that the DTPS-quasi-Armendariz rings are closed under direct sums,upper triangular matrix rings,full matrix rings and Morita invariance.Various classes of non-semiprime DTPS-quasi-Armendariz rings are provided,and a number of properties of this generalization are established.Some characterizations for the differential inverse power series ring R[[x^-1;δ]]to be quasi-Baer,generalized quasi-Baer,primary,nilary,reflexive,ideal-symmetric and left AIP are conncluded,whereδis a derivation on the ring R.Finally,miscellaneous examples to illustrate and delimit the theory are given.展开更多
文摘This paper mainly studies some properties of skew polynomial ring related to Morita invariance, Armendariz and (quasi)-Baer. First, we show that skew polynomial ring has no Morita invariance by the counterexample. Then we prove a necessary condition that skew polynomial ring constitutes Armendariz ring. We lastly investigate that condition of skew polynomial ring is a (quasi)-Baer ring, and verify that the conditions is necessary, but not sufficient by example and counterexample.
文摘In this paper we continue the study of various ring theoretic properties of Morita contexts.Necessary and sufficient conditions are obtained for a general Morita context or a trivial Morita context or a formal triangular matrix ring to satisfy a certain ring property which is among being Kasch,completely primary,quasi-duo,2-primal,NI,semiprimitive,projective-free,etc.We also characterize when a general Morita context is weakly principally quasi-Baer or strongly right mininjective.
基金Foundation item： the National Natural Science Foundation of China （No. 10671122）.
文摘In this paper,we give the equivalent characterizations of principally quasi-Baer modules,and show that any direct summand of a principally quasi-Baer module inherits the property and any finite direct sum of mutually subisomorphic principally quasi-Baer modules is also principally quasi-Baer.Moreover,we prove that left principally quasi-Baer rings have Morita invariant property.Connections between Richart modules and principally quasi-Baer modules are investigated.
文摘In this paper, the (quasi-)Baerness of skew group ring and fixed ring is investigated. The following two results are obtained: if R is a simple ring with identity and G an outer automorphism group, then R G is a Baer ring;if R is an Artinian simple ring with identity and G an outer automorphism group, then RG is a Baer ring. Moreover, by decomposing Morita Context ring and Morita Context Theory, we provided several conditions of Morita Context ring, which is formed of skew group ring and fixed ring, to be (quasi-)Baer ring.
基金Supported by National Natural Science Foundation of China (Grant No.10961021)the Cultivation Fund of the Key Scientific and Technical Innovation Project,Ministry of Education of China
文摘Let R be a ring. We consider left （or right） principal quasi-Baerness of the left skew formal power series ring R[[x;α]] over R where a is a ring automorphism of R. We give a necessary and sufficient condition under which the ring R[[x; α]] is left （or right） principally quasi-Baer. As an application we show that R[[x]] is left principally quasi-Baer if and only if R is left principally quasi- Baer and the left annihilator of the left ideal generated by any countable family of idempotents in R is generated by an idempotent.
文摘A generalization of semiprime rings and right p.q.-Baer rings,which we call quasi-Armendariz rings of differential inverse power series type(or simply,DTPS-quasi-Armendariz),is introduced and studied.It is shown that the DTPS-quasi-Armendariz rings are closed under direct sums,upper triangular matrix rings,full matrix rings and Morita invariance.Various classes of non-semiprime DTPS-quasi-Armendariz rings are provided,and a number of properties of this generalization are established.Some characterizations for the differential inverse power series ring R[[x^-1;δ]]to be quasi-Baer,generalized quasi-Baer,primary,nilary,reflexive,ideal-symmetric and left AIP are conncluded,whereδis a derivation on the ring R.Finally,miscellaneous examples to illustrate and delimit the theory are given.
