The $X$-semiprimeness of Rings
| Autor: | Călugăreanu, Grigore, Lee, Tsiu-Kwen, Matczuk, Jerzy |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | For a nonempty subset $X$ of a ring $R$, the ring $R$ is called $X$-semiprime if, given $a\in R$, $aXa=0$ implies $a=0$. This provides a proper class of semiprime rings. First, we clarify the relationship between idempotent semiprime and unit-semiprime rings. Secondly, given a Lie ideal $L$ of a ring $R$, we offer a criterion for $R$ to be $L$-semiprime. For a prime ring $R$, we characterizes Lie ideals $L$ of $R$ such that $R$ is $L$-semiprime. Moreover, $X$-semiprimeness of matrix rings, prime rings (with a nontrivial idempotent), semiprime rings, regular rings, and subdirect products are studied. Comment: Comments welcome |
| Databáze: | arXiv |
| Externí odkaz: |
|