■-STABLE 模

■-STABLE 模 ■-STABLE MODULES 徐邦腾 Xu Bangteng 1 first-author 湖北黄冈师专 数学系1988届研究生 湖北黄冈师专 数学系1988届研究生 Department of mathematics, Wuhan University Department of mathematics, Wuhan University 本文引入了■-stable模的概念,讨论了■-stable模的刻画和若干性质,并利用■-stable模来研究线性拓扑的稳定性,给出了一个线性拓扑是稳定的充要条件及Noether环上Artin-Rees模的一个重要性质,改进和推广了P.Gabreil、B.Stenstrom等人的工作。 In this paper we have introduced the notion of a -stable module, discu-ssed its characterizations and properties, and studied the stability of linear topologies by means of -stable modules. We have given a sufficient and ne-cessary condition for a linear topology to be stable, and an important prop-erty of Artin-Recs modules over Noetherian rings. Some results of P. Gab-riel〔1〕and B. Stenstrm〔8〕have been improved and developed in our paper. 线性拓扑 preradieal ■-stable 模 稳定性 ■-pretorsion模 Artin-Rees模 linear topologies preradicals ■-stable modules stability ■-pretorsion modules Artin-Rees modules 1988-04-01 2021-04-01 4