Let us call a ring R (without identity) to be right symmetric if for any triple a,b,c,∈R?abc = 0 then acb = 0. Such rings are neither symmetric nor reversible (in general) but are semicommutative. With an idempotent ...Let us call a ring R (without identity) to be right symmetric if for any triple a,b,c,∈R?abc = 0 then acb = 0. Such rings are neither symmetric nor reversible (in general) but are semicommutative. With an idempotent they take care of the sheaf representation as obtained by Lambek. Klein 4-rings and their several generalizations and extensions are proved to be members of such class of rings. An extension obtained is a McCoy ring and its power series ring is also proved to be a McCoy ring.展开更多
Let R be a ring and (S,≤) a strictly ordered monoid. In this paper, we deal with a new approach to reflexive property for rings by using nilpotent elements, in this direction we introduce the notions of generalized p...Let R be a ring and (S,≤) a strictly ordered monoid. In this paper, we deal with a new approach to reflexive property for rings by using nilpotent elements, in this direction we introduce the notions of generalized power series reflexive and nil generalized power series reflexive, respectively. We obtain various necessary or sufficient conditions for a ring to be generalized power series reflexive and nil generalized power series reflexive. Examples are given to show that, nil generalized power series reflexive need not be generalized power series reflexive and vice versa, and nil generalized power series reflexive but not semicommutative are presented. We proved that, if R is a left APP-ring, then R is generalized power series reflexive, and R is nil generalized power series reflexive if and only if R/I is nil generalized power series reflexive. Moreover, we investigate ring extensions which have roles in ring theory.展开更多
In This paper, the concept of weakly dual ring is introduced, which is a proper generalization of the dual ring. If R is a right weakly dual ring, then (1) Z(RR) = J(R); (2) If R is also a zero-division power ring, th...In This paper, the concept of weakly dual ring is introduced, which is a proper generalization of the dual ring. If R is a right weakly dual ring, then (1) Z(RR) = J(R); (2) If R is also a zero-division power ring, then R is a right AP-injective ring. In addition, some properties of weakly dual rings are given.展开更多
本文阐述了两例犬血管环异常(vascular ring anomaly,VRA)的CT血管造影(CT angiography,CTA)诊断及手术治疗。通过术前对患犬进行CTA诊断,进行经左侧第4肋间开胸动脉韧带切断的手术治疗,并在术后对病例1进行食道球囊扩张。CTA显示两只...本文阐述了两例犬血管环异常(vascular ring anomaly,VRA)的CT血管造影(CT angiography,CTA)诊断及手术治疗。通过术前对患犬进行CTA诊断,进行经左侧第4肋间开胸动脉韧带切断的手术治疗,并在术后对病例1进行食道球囊扩张。CTA显示两只犬均存在持久性右主动脉弓(persistent right aortic arch,PRAA),并分别伴有右侧颈动脉异位发育和持久性左前腔静脉。手术治疗后,食道狭窄基本得到纠正,返流消失。CTA可对VRA进行更精确地诊断,并有助于制订具体手术方案;犬PRAA的手术治疗效果良好。展开更多
Let R be a ring and e,g in E(R),the set of idempotents of R.Then R is called(g,e)-symmetric if abc=0 implies gacbe=0 for any a,b,c∈R.Clearly,R is an e-symmetric ring if and only if R is a(1,e)-symmetric ring;in parti...Let R be a ring and e,g in E(R),the set of idempotents of R.Then R is called(g,e)-symmetric if abc=0 implies gacbe=0 for any a,b,c∈R.Clearly,R is an e-symmetric ring if and only if R is a(1,e)-symmetric ring;in particular,R is a symmetric ring if and only if R is a(1,1)-symmetric ring.We show that e∈E(R)is left semicentral if and only if R is a(1−e,e)-symmetric ring;in particular,R is an Abel ring if and only if R is a(1−e,e)-symmetric ring for each e∈E(R).We also show that R is(g,e)-symmetric if and only if ge∈E(R),geRge is symmetric,and gxye=gxeye=gxgye for any x,y∈R.Using e-symmetric rings,we construct some new classes of rings.展开更多
文摘Let us call a ring R (without identity) to be right symmetric if for any triple a,b,c,∈R?abc = 0 then acb = 0. Such rings are neither symmetric nor reversible (in general) but are semicommutative. With an idempotent they take care of the sheaf representation as obtained by Lambek. Klein 4-rings and their several generalizations and extensions are proved to be members of such class of rings. An extension obtained is a McCoy ring and its power series ring is also proved to be a McCoy ring.
文摘Let R be a ring and (S,≤) a strictly ordered monoid. In this paper, we deal with a new approach to reflexive property for rings by using nilpotent elements, in this direction we introduce the notions of generalized power series reflexive and nil generalized power series reflexive, respectively. We obtain various necessary or sufficient conditions for a ring to be generalized power series reflexive and nil generalized power series reflexive. Examples are given to show that, nil generalized power series reflexive need not be generalized power series reflexive and vice versa, and nil generalized power series reflexive but not semicommutative are presented. We proved that, if R is a left APP-ring, then R is generalized power series reflexive, and R is nil generalized power series reflexive if and only if R/I is nil generalized power series reflexive. Moreover, we investigate ring extensions which have roles in ring theory.
基金Foundationitem:The NNSP(19971073) of China and the NSF of Yangzhou University
文摘In This paper, the concept of weakly dual ring is introduced, which is a proper generalization of the dual ring. If R is a right weakly dual ring, then (1) Z(RR) = J(R); (2) If R is also a zero-division power ring, then R is a right AP-injective ring. In addition, some properties of weakly dual rings are given.
文摘本文阐述了两例犬血管环异常(vascular ring anomaly,VRA)的CT血管造影(CT angiography,CTA)诊断及手术治疗。通过术前对患犬进行CTA诊断,进行经左侧第4肋间开胸动脉韧带切断的手术治疗,并在术后对病例1进行食道球囊扩张。CTA显示两只犬均存在持久性右主动脉弓(persistent right aortic arch,PRAA),并分别伴有右侧颈动脉异位发育和持久性左前腔静脉。手术治疗后,食道狭窄基本得到纠正,返流消失。CTA可对VRA进行更精确地诊断,并有助于制订具体手术方案;犬PRAA的手术治疗效果良好。
基金supported by the Foundation of Natural Science of China(12301029,11171291)Natural Science Fund for Colleges and Universities in Jiangsu Province(11KJB110019 and 15KJB110023).
文摘Let R be a ring and e,g in E(R),the set of idempotents of R.Then R is called(g,e)-symmetric if abc=0 implies gacbe=0 for any a,b,c∈R.Clearly,R is an e-symmetric ring if and only if R is a(1,e)-symmetric ring;in particular,R is a symmetric ring if and only if R is a(1,1)-symmetric ring.We show that e∈E(R)is left semicentral if and only if R is a(1−e,e)-symmetric ring;in particular,R is an Abel ring if and only if R is a(1−e,e)-symmetric ring for each e∈E(R).We also show that R is(g,e)-symmetric if and only if ge∈E(R),geRge is symmetric,and gxye=gxeye=gxgye for any x,y∈R.Using e-symmetric rings,we construct some new classes of rings.
