Morita Duality for the Rings of Generalized Power Series  

作　　者：LIU Zhong Kui Department of Mathematics.Northwest Normal University.Lanzhou 730070.P.R.China [e-mail] 

出　　处：《Acta Mathematica Sinica,English Series》2002年第2期245-252,共8页数学学报（英文版）

基　　金：supported by National Natural Science Foundation of China(10171082);Foundation for University Key Teacher;the Ministry of Education(GG-110-10736-1001)

摘　　要：Let A,B be associative rings with identity,and(S.≤)a strictly totally ordered monoid which is also artinian and finitely generated.For any bimodule AaMB. we show that the bimodule [[A^(S.≤)]][M^(S.≤)][[B^(S.≤)]]defines a Morita duality if and only if _AM_B defines a Morita duality and A is left noetherian.B is right noetherian.As a corollary,it.is shown that the ring[[A^(S.≤)]]of generalized power series over A has a Morita duality if and only if A is a left noetherian ring with a Morita duality induced by a bimodule _AM_B such that B is right noetherian.Let A,B be associative rings with identity,and(S.≤)a strictly totally ordered monoid which is also artinian and finitely generated.For any bimodule AaMB. we show that the bimodule [[A^(S.≤)]][M^(S.≤)][[B^(S.≤)]]defines a Morita duality if and only if _AM_B defines a Morita duality and A is left noetherian.B is right noetherian.As a corollary,it.is shown that the ring[[A^(S.≤)]]of generalized power series over A has a Morita duality if and only if A is a left noetherian ring with a Morita duality induced by a bimodule _AM_B such that B is right noetherian.

关 键 词：Morita duality Left linearly compact module Ring of generalized power series 

分 类 号：O153.3[理学—数学]