{"ID":23595662,"CreatedAt":"2026-09-18T05:42:42.291333095Z","UpdatedAt":"2026-09-18T05:42:42.291333095Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.20076","arxiv_id":"2609.20076","title":"On $\\ast$-Reversible and Generalized $\\ast$-Reversible Rings","abstract":"Let $R$ be a $\\ast$-ring with $a,b\\in R$. A ring $R$ is said to be $\\ast$-reversible if $ab=0$ implies $b^{\\ast}a=0$. In this paper, we first establish several new characterizations of $\\ast$-reversible rings and reversible rings. In particular, we prove that $\\ast$-reversible rings coincide with $\\ast$-symmetric rings. Using these characterizations, we introduce two new classes of generalized $\\ast$-reversible rings: pro-$\\ast$-reversible rings and nil-$\\ast$-reversible rings. A ring $R$ is called pro-$\\ast$-reversible if $ab\\in P(R)$ implies $b^{\\ast}a\\in P(R)$, and $R$ is nil-$\\ast$-reversible if for every $c\\in N(R)$, $cb=0$ yields both $b^{\\ast}c=0$ and $cb^{\\ast}=0$. The basic properties and characterizations of pro-$\\ast$-reversible and nil-$\\ast$-reversible rings are investigated. The interrelationships among all these ring classes are considered. The related examples to distinguish these rings are constructed.","short_abstract":"Let $R$ be a $\\ast$-ring with $a,b\\in R$. A ring $R$ is said to be $\\ast$-reversible if $ab=0$ implies $b^{\\ast}a=0$. In this paper, we first establish several new characterizations of $\\ast$-reversible rings and reversible rings. In particular, we prove that $\\ast$-reversible rings coincide with $\\ast$-symmetric rings...","url_abs":"https://arxiv.org/abs/2609.20076","url_pdf":"https://arxiv.org/pdf/2609.20076v1","authors":"[\"Huaxi Chen\",\"Long Wang\",\"Honglin Zou\"]","published":"2026-09-17T11:34:44Z","proceeding":"math.RA","tasks":"[\"math.RA\"]","methods":"[]","has_code":false}