Abstract

Characterizations of Morita context rings satisfying various additional ring properties, including reflexive, semiprime, prime, NI, weakly 2-primal and 2-primal, are given. The connections between the characterizations of reflexive, semiprime and prime Morita context rings are outlined and shown to be related to torsionless and faithful modules. Similarly, the characterizations of NI, weakly 2-primal and 2-primal are shown to be related. In particular, a characterization of NI Morita context rings is determined to be equivalent to Köthe’s conjecture.

中文翻译：

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某些 Morita 上下文环的特征

摘要

给出了满足各种附加环属性的 Morita 上下文环的特征，包括自反、半素数、素数、NI、弱 2-primal 和 2-primal。概述了自反、半素和素 Morita 上下文环的特征之间的联系，并显示出与无扭转和忠实模块有关。类似地，NI、弱 2-primal 和 2-primal 的特征显示是相关的。特别是，NI Morita 上下文环的特征被确定为等价于 Köthe 猜想。