Symmetrization in Clean and Nil-Clean Rings
| Autor: | Peter V. Danchev |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Physics
symmetrization General Computer Science Mechanical Engineering General Mathematics lcsh:Mathematics Mathematics::Rings and Algebras Computational Mechanics lcsh:QA1-939 Mechanics of Materials Mathematics::K-Theory and Homology Condensed Matter::Superconductivity Symmetrization r-clean rings Atomic physics l-clean rings d-clean rings weakly nil(-)clean rings |
| Zdroj: | Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика, Vol 20, Iss 2, Pp 154-160 (2020) |
| ISSN: | 2541-9005 1816-9791 |
| Popis: | We introduce and investigate D-clean and D-nil-clean rings as well as some other closely related symmetric versions of cleanness and nil-cleanness. A comprehensive structural characterization is given for these symmetrically clean and symmetrically nil-clean rings in terms of Jacobson radical and its quotient. It is proved that strongly clean (resp., strongly nil-clean) rings are always D-clean (resp., D-nil-clean).Our results corroborate our recent findings published in Bull. Irkutsk State Univ., Math. (2019) and Turk. J. Math. (2019). We also show that weakly nil-clean rings defined as in Danchev-McGovern (J. Algebra, 2015) and Breaz - Danchev - Zhou (J. Algebra Appl., 2016) are actually weakly nil clean in the sense of Danchev-Ster (Taiwanese J. Math., 2015). This answers the question of the reviewer D. Khurana (Math. Review, 2017). |
| Databáze: | OpenAIRE |
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