关于 n-f-Semiclean 环

IF 0.8 4区综合性期刊 Q3 MULTIDISCIPLINARY SCIENCES

Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Pub Date : 2024-11-04 DOI:10.1007/s40010-024-00897-5

Avanish Kumar Chaturvedi, Sandeep Kumar, Nirbhay Kumar

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引用次数: 0

摘要

n-f-semiclean 环类介于 n-f-clean 环类和\((n+1)\)-f-clean 环类之间。我们根据 n-f-semiclean 环的皮尔斯茎给出了它的特征。我们证明，如果 e 是一个幂等元素，使得 eRe 和 \((1-e)R(1-e)\) 是 n-f-semiclean 的，那么 R 就是 n-f-semiclean 的。此外，我们还发现 n-f-semiclean 环的矩阵环也是 n-f-semiclean 环。我们用 n-f-semiclean 环的扩展环给出了 n-f-semiclean 环的一些特征。

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On n-f-Semiclean Rings

The class of n-f-semiclean rings lies between the classes of n-f-clean rings and \((n+1)\)-f-clean rings. We give a characterization of n-f-semiclean rings in terms of its Pierce stalks. We prove that if e is an idempotent such that eRe and \((1-e)R(1-e)\) are n-f-semiclean, then R is n-f-semiclean. Further, we find that matrix rings of an n-f-semiclean ring are n-f-semiclean. We give some characterizations of n-f-semiclean rings in terms of their extension rings.