On Strongly pi-Regular Rings with Involution
Recall that a ring R is called strongly pi-regular if, for every a in R, there is a positive integer n, depending on a, such that a^n belongs to the intersection of a^{n+1}R and Ra^{n+1}. In this paper we give a further study of the notion of a strongly pi-star-regular ring, which is the star-versio...
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| Published in | Communications in Mathematics Vol. 31 (2023), Issue 1 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
2023
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| Online Access | Get full text |
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| Summary: | Recall that a ring R is called strongly pi-regular if, for every a in R,
there is a positive integer n, depending on a, such that a^n belongs to the
intersection of a^{n+1}R and Ra^{n+1}. In this paper we give a further study of
the notion of a strongly pi-star-regular ring, which is the star-version of
strongly pi-regular rings and which was originally introduced by Cui-Wang in J.
Korean Math. Soc. (2015). We also establish various properties of these rings
and give several new characterizations in terms of (strong) pi-regularity and
involution. Our results also considerably extend recent ones in the subject due
to Cui-Yin in Algebra Colloq. (2018) proved for pi-star-regular rings and due
to Cui-Danchev in J. Algebra Appl. (2020) proved for star-periodic rings. |
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| ISSN: | 2336-1298 2336-1298 |
| DOI: | 10.46298/cm.10273 |