On ∗-Reversible and Generalized ∗-Reversible Rings
Abstract
Let R be a ∗-ring with a,b∈ R. A ring R is said to be ∗-reversible if ab=0 implies b∗a=0. In this paper, we first establish several new characterizations of ∗-reversible rings and reversible rings. In particular, we prove that ∗-reversible rings coincide with ∗-symmetric rings. Using these characterizations, we introduce two new classes of generalized ∗-reversible rings: pro-∗-reversible rings and nil-∗-reversible rings. A ring R is called pro-∗-reversible if ab∈ P(R) implies b∗a∈ P(R), and R is nil-∗-reversible if for every c∈ N(R), cb=0 yields both b∗c=0 and cb∗=0. The basic properties and characterizations of pro-∗-reversible and nil-∗-reversible rings are investigated. The interrelationships among all these ring classes are considered. The related examples to distinguish these rings are constructed.
Related
- On Reversible Rings, Their Generalization and Quasi-Idempotent Elements
- Commutativity Criteria and Structural Properties of Prime Near-Rings Admitting Right Generalized Derivations on Specific Ideals
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BibTeX
@misc{chen2026reversible,
title = {{On $\ast$-Reversible and Generalized $\ast$-Reversible Rings}},
author = {Huaxi Chen and Long Wang and Honglin Zou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20076},
eprint = {2609.20076},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20076},
}
RIS
TY - UNPB
TI - On ∗-Reversible and Generalized ∗-Reversible Rings
AU - Huaxi Chen
AU - Long Wang
AU - Honglin Zou
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20076
UR - https://arxiv.org/abs/2609.20076
AB - Let R be a ∗-ring with a,b∈ R. A ring R is said to be ∗-reversible if ab=0 implies b^∗a=0. In this paper, we first establish several new characterizations of ∗-reversible rings and reversible rings. In particular, we prove that ∗-reversible rings coincide with ∗-symmetric rings. Using these characterizations, we introduce two new classes of generalized ∗-reversible rings: pro-∗-reversible rings and nil-∗-reversible rings. A ring R is called pro-∗-reversible if ab∈ P(R) implies b^∗a∈ P(R), and R is nil-∗-reversible if for every c∈ N(R), cb=0 yields both b^∗c=0 and cb^∗=0. The basic properties and characterizations of pro-∗-reversible and nil-∗-reversible rings are investigated. The interrelationships among all these ring classes are considered. The related examples to distinguish these rings are constructed.
ER -