摘要
设A,B是有单位元的环, (S,≤)是有限生成的Artin的严格全序幺半群, AMB是双模.本文证明了双模[[AS,≤]][MS,≤][[BS,≤]]定义一个Morita对偶当且仅当 AMB定义一个Morita对偶且A是左noether的,B是右noether的.因此A上的广 义幂级数环[[AS,≤]]具有Morita对偶当且仅当A是左noether的且具有由双模AMB 诱导的Morita对偶,使得B是右noether的.
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 AMB, we show that the bimodule [[AS,≤]][MS,≤][[BS,≤]] defines a Morita duality if and only if AMB defines a Morita duality and A is left noetherian, B is right noetherian. As a corollary, it is shown that the ring [[AS,≤]] 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 AMB such that B is right noetherian.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2005年第2期397-402,共6页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金(10171082)教育部科技创新工程重大项目培育资金 TRAPOYT资助项目
关键词
MORITA对偶
左线性紧模
广义幂级数环
Morita duality
Left linearly compact module
Ring of generalized power series
