rings with involution
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2022 ◽  
Vol 29 (01) ◽  
pp. 39-52
Author(s):  
Long Wang ◽  
Dijana Mosić ◽  
Yuefeng Gao

In this paper, we mainly give characterizations of EP elements in terms of equations. In addition, a related notion named a central EP element is defined and investigated. Finally, we focus on characterizations of a generalized EP element, i.e., [Formula: see text]-DMP element.



2022 ◽  
pp. 1-12
Author(s):  
Mohammad Salahuddin Khan ◽  
Shakir Ali ◽  
Mohammed Ayedh


Author(s):  
Jose Brox ◽  
Esther García ◽  
Miguel Gómez Lozano ◽  
Rubén Muñoz Alcázar ◽  
Guillermo Vera de Salas




2021 ◽  
Vol 28 (03) ◽  
pp. 367-378
Author(s):  
Jian Cui ◽  
Guoli Xia ◽  
Yiqiang Zhou

A [Formula: see text]-ring [Formula: see text] is called a nil [Formula: see text]-clean ring if every element of [Formula: see text] is a sum of a projection and a nilpotent. Nil [Formula: see text]-clean rings are the [Formula: see text]-version of nil-clean rings introduced by Diesl. This paper is about the nil [Formula: see text]-clean property of rings with emphasis on matrix rings. We show that a [Formula: see text]-ring [Formula: see text] is nil [Formula: see text]-clean if and only if [Formula: see text] is nil and [Formula: see text] is nil [Formula: see text]-clean. For a 2-primal [Formula: see text]-ring [Formula: see text], with the induced involution given by[Formula: see text], the nil [Formula: see text]-clean property of [Formula: see text] is completely reduced to that of [Formula: see text]. Consequently, [Formula: see text] is not a nil [Formula: see text]-clean ring for [Formula: see text], and [Formula: see text] is a nil [Formula: see text]-clean ring if and only if [Formula: see text] is nil, [Formula: see text]is a Boolean ring and [Formula: see text] for all [Formula: see text].





2021 ◽  
Vol 42 (4) ◽  
pp. 613-624
Author(s):  
Huihui Zhu ◽  
Qing-Wen Wang


2021 ◽  
Vol 26 (2) ◽  
Author(s):  
Ikram Saed

    Let M be a -ring with involution . In this paper , we will introduce the concept of symmetric left(right) reverse *-4-centralizer of M . Then, we proved that the  4-additive mapping  T:MxMxMxMM is a reverse *-4-centralizer of M under certain conditions .



2021 ◽  
pp. 1-15
Author(s):  
A. Mamouni ◽  
L. Oukhtite ◽  
M. Zerra


2021 ◽  
Vol 45 (02) ◽  
pp. 225-236
Author(s):  
MUZIBUR RAHMAN MOZUMDER ◽  
ADNAN ABBASI ◽  
NADEEM AHMAD DAR ◽  
AFTAB HUSSAIN SHAH

The purpose of this paper is to study pair of left centralizers in prime rings with involution satisfying certain identities.



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