Nilpotent Elements and Nil-Reflexive Property of Generalized Power Series Rings  

作　　者：Eltiyeb Ali Eltiyeb Ali(Department of Mathematics, Faculty of Education, University of Khartoum, Khartoum, Sudan;Department of Mathematics, Faculty of Science and Arts, Najran University, Najran, KSA)

机构地区：[1]Department of Mathematics, Faculty of Education, University of Khartoum, Khartoum, Sudan [2]Department of Mathematics, Faculty of Science and Arts, Najran University, Najran, KSA

出　　处：《Advances in Pure Mathematics》2022年第11期676-692,共17页理论数学进展（英文）

摘　　要：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.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.

关 键 词：Left APP-Ring Generalized Power Series Reflexive Ring Nil Generalized Power Series Reflexive Ring S-Quasi Armendariz Ring Semiprime Ring Semicommutative Ring 

分 类 号：O17[理学—数学]