Rings in Which Every Element Is a Sum of a Nilpotent and Three 7-Potents
| Autor: | Yanyuan Wang, Xinsong Yang |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | International Journal of Mathematics and Mathematical Sciences, Vol 2024 (2024) |
| Druh dokumentu: | article |
| ISSN: | 1687-0425 |
| DOI: | 10.1155/2024/4402496 |
| Popis: | In this article, we define and discuss strongly S3,7 nil-clean rings: every element in a ring is the sum of a nilpotent and three 7-potents that commute with each other. We use the properties of nilpotent and 7-potent to conduct in-depth research and a large number of calculations and obtain a nilpotent formula for the constant a. Furthermore, we prove that a ring R is a strongly S3,7 nil-clean ring if and only if R=R1⊕R2⊕R3⊕R4⊕R5⊕R6, where R1, R2, R3, R4, R5, and R6 are strongly S3,7 nil-clean rings with 2∈NilR1, 3∈NilR2, 5∈NilR3, 7∈NilR4, 13∈NilR5, and 19∈NilR6. The equivalent conditions of strongly S3,7 nil-clean rings in some cases are discussed. |
| Databáze: | Directory of Open Access Journals |
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