软弱和CO-WEAK贝尔模块:موديلاتبييرالضعيفةوالضعيفةالمرافقة

Eaman Al-Khouja, Magd Alfakhory, Hamza Hakmi Eaman Al-Khouja, Magd Alfakhory, Hamza Hakmi
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引用次数: 0

摘要

本文研究了弱Baer环和弱Rickart环及模的概念。我们得到了弱Rickart环的许多特征,并给出了它们的性质。研究了弱Rickart(弱Baer)模与其自同态环之间的关系。证明了在其自同态环上不存在无限非零正交幂等元集的弱Baer模就是Baer模。此外,半射影弱Rickart模的自同态环是半幂幂的,半内射协弱Rickart模的自同态环是半幂幂的。进一步证明了一个自由模是弱贝尔的当且仅当其自同态环是左弱贝尔的。
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WEAK and CO-WEAK BAER MODULES: موديلات بيير الضعيفة والضعيفة المرافقة
The object of this paper is study the notions of weak Baer and weak Rickart rings and modules. We obtained many characterizations of weak Rickart rings and provide their properties. Relations ship between a weak Rickart (weak Baer) module and its endomorphism ring are studied. We proved that a weak Baer module with no infinite set of nonzero orthogonal idempotent elements in its endomorphism ring is precisely a Baer module. In addition, the endomorphism ring of a semi-projective weak Rickart module is semi-potent and the endomorphism ring of a semi-injective coweak Rickart module is semi-potent. Furthermore, we show that a free module is weak Baer if and only if its endomorphism ring is left weak Baer.
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