This paper gives some results on Strong-Armendariz rings and the Ore-extensions R[x,x^-1;α] of Bare, PP and PS rings. And the main two results are： （1） R is a Bear （PP） ring if and only if R[[x]] is a Baer （PP...This paper gives some results on Strong-Armendariz rings and the Ore-extensions R[x,x^-1;α] of Bare, PP and PS rings. And the main two results are： （1） R is a Bear （PP） ring if and only if R[[x]] is a Baer （PP） ring; （2） If R is an α-rigid ring, then R is a Baer （PP, PS） ring if and only if R[x, x^-1; α] is a Baer （PP, PS） ring.展开更多
We introduce the notions of IDS modules, IP modules, and Baer＊ modules, which are new generalizations of von Neumann regular rings, PP rings, and Baer rings, respectively, in a general module theoretic setting. We ob...We introduce the notions of IDS modules, IP modules, and Baer＊ modules, which are new generalizations of von Neumann regular rings, PP rings, and Baer rings, respectively, in a general module theoretic setting. We obtain some characterizations and properties of IDS modules, IP modules and Baer modules. Some important classes of rings are characterized in terms of IDS modules, IP modules, and Baer modules.展开更多
基金the Program for New Century Excellent Talents in University(04-0522),and the National Natural Science Foundation of China(10571153)
文摘This paper gives some results on Strong-Armendariz rings and the Ore-extensions R[x,x^-1;α] of Bare, PP and PS rings. And the main two results are： （1） R is a Bear （PP） ring if and only if R[[x]] is a Baer （PP） ring; （2） If R is an α-rigid ring, then R is a Baer （PP, PS） ring if and only if R[x, x^-1; α] is a Baer （PP, PS） ring.
基金This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11171149, 11371187）, Jiangsu 333 Project, and Jiangsu Six Major Talents Peak Project.
文摘We introduce the notions of IDS modules, IP modules, and Baer＊ modules, which are new generalizations of von Neumann regular rings, PP rings, and Baer rings, respectively, in a general module theoretic setting. We obtain some characterizations and properties of IDS modules, IP modules and Baer modules. Some important classes of rings are characterized in terms of IDS modules, IP modules, and Baer modules.
