主拟-Baer模

Principally Quasi-Baer Modules

中文关键词:  主拟-Baer环(模)  自同态环  零化子  左(右)半中心幂等元.

英文关键词:principally quasi-Baer rings (modules)  endomorphism rings  annihilators  semicentral idempotents.

中文摘要:

      本文引入左主拟-Baer模的概念, 并给出了左主拟-Baer模的等价刻画条件. 探讨了左主拟-Baer模的一些性质, 例如: 左主拟-Baer模对直和项封闭, 互为子同构的左主拟-Baer模的直和仍然是左主拟-Baer模; 并证明了左主拟-Baer环具有Morita等价不变性.此外, 我们还探讨了左Richart模与左主拟-Baer模之间关系.

英文摘要:

      In this paper, we give the equivalent characterizations of principally quasi-Baer modules, and show that any direct summand of a principally quasi-Baer module inherits the property and any finite direct sum of mutually subisomorphic principally quasi-Baer modules is also principally quasi-Baer. Moreover, we prove that left principally quasi-Baer rings have Morita invariant property. Connections between Richart modules and principally quasi-Baer modules are investigated.