On Annihilator Ideals of Pseudo-differential Operator Rings  

作　　者：R. Manaviyat A. Moussavi 

机构地区：[1]Department of Pure Mathematics, Faculty of Mathematical Sciences Tarbiat Modares University, P.O. Box 14115-134, Tehran, Iran

出　　处：《Algebra Colloquium》2015年第4期607-620,共14页代数集刊（英文版）

摘　　要：Let R be a ring with a derivation 5 and R（（x-1;5）） denote the pseudo- differential operator ring over R. We study the relations between the set of annihilators in R and the set of annihilators in R（（x-1; 5））. Among applications, it is shown that for an Armendariz ring R of pseudo-differential operator type, the ring R（（x-1; 5）） is Baer （resp., quasi-Baer, PP, right zip） if and only if R is a Baer （resp., quasi-Baer, PP, right zip） ring. For a 5-weakly rigid ring R, R（（x-1;5）） is a left p.q.-Baer ring if and only if R is left p.q.-Baer and every countable subset of left semicentral idempotents of R has a generalized countable join in R.Let R be a ring with a derivation 5 and R（（x-1;5）） denote the pseudo- differential operator ring over R. We study the relations between the set of annihilators in R and the set of annihilators in R（（x-1; 5））. Among applications, it is shown that for an Armendariz ring R of pseudo-differential operator type, the ring R（（x-1; 5）） is Baer （resp., quasi-Baer, PP, right zip） if and only if R is a Baer （resp., quasi-Baer, PP, right zip） ring. For a 5-weakly rigid ring R, R（（x-1;5）） is a left p.q.-Baer ring if and only if R is left p.q.-Baer and every countable subset of left semicentral idempotents of R has a generalized countable join in R.

关 键 词：pseudo-differential operator ring annihilator ideal Baer ring quasi-Baerring Armendariz-like condition 

分 类 号：O153.3[理学—数学] O175.3[理学—基础数学]