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Tien N. Q., KOŞAN M. T., Quynh T. C.
Journal of Algebra and its Applications, 2024 (SCI-Expanded)
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Publication Type:
Article / Article
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Publication Date:
2024
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Doi Number:
10.1142/s0219498825503177
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Journal Name:
Journal of Algebra and its Applications
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Journal Indexes:
Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
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Keywords:
(semi)potent ring, nilpotent element, quasi-nilpotent element, UJ-ring, Unit element, UU-ring, ΔU-ring
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Gazi University Affiliated:
Yes
Abstract
This paper is concerned with the investigation of those rings R whose invertible elements are sums 1 + a for an element a ∈ R such that 1 − au is invertible for all invertible u ∈ R with au = ua. UJ-rings and UQ-rings (and hence UU-rings) are examples of such rings. We prove that such rings are Dedekind finite, and for semisimple rings R, R ∼= F2 × F2 × · · · × F2. In case R is also a semipotent ring, it is shown that R/J(R) is a Boolean ring.