Prime rings with involution involving left multipliers
Abstract Let R be a prime ring of characteristic different from 2 with involution ’∗’ of the second kind and n ≥ 1 be a fixed positive integer. In the present paper it is shown that if R admits nonzero left multipliers S and T , then the following conditions are equivalent: (i)R is commutative, (ii) Tn([x, x∗]) ∈ Z(R) for all x ∈ R; (iii) Tn(x ◦ x∗) ∈ Z(R) for all x ∈ R; (iv) [S(x), T (x∗)] ∈ Z(R) for all x ∈ R; (v) [S(x), T (x∗)] − (x ◦ x∗) ∈ Z(R) for all x ∈ R; (vi) S(x) ◦ T (x∗) ∈ Z(R) for all x ∈ R; (vii) S(x) ◦ T (x∗) − [x, x∗] ∈ Z(R) for all x ∈ R. The existence of hypotheses in various theorems have been justified by the examples.
Main Authors:  , 

Format:  Digital revista 
Language:  English 
Published: 
Universidad Católica del Norte, Departamento de Matemáticas
2020

Online Access:  http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S071609172020000200341 
Tags: 
Add Tag
No Tags, Be the first to tag this record!

id 
oai:scielo:S071609172020000200341 

record_format 
ojs 
spelling 
oai:scielo:S07160917202000020034120200506Prime rings with involution involving left multipliersBoua,AbdelkarimAshraf,Mohammad Prime ring Derivation Multiplier Involution Commutativity Abstract Let R be a prime ring of characteristic different from 2 with involution ’∗’ of the second kind and n ≥ 1 be a fixed positive integer. In the present paper it is shown that if R admits nonzero left multipliers S and T , then the following conditions are equivalent: (i)R is commutative, (ii) Tn([x, x∗]) ∈ Z(R) for all x ∈ R; (iii) Tn(x ◦ x∗) ∈ Z(R) for all x ∈ R; (iv) [S(x), T (x∗)] ∈ Z(R) for all x ∈ R; (v) [S(x), T (x∗)] − (x ◦ x∗) ∈ Z(R) for all x ∈ R; (vi) S(x) ◦ T (x∗) ∈ Z(R) for all x ∈ R; (vii) S(x) ◦ T (x∗) − [x, x∗] ∈ Z(R) for all x ∈ R. The existence of hypotheses in various theorems have been justified by the examples.info:eurepo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.39 n.2 202020200401text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S071609172020000200341en10.22199/issn.071762792020020021 
institution 
SCIELO 
collection 
OJS 
country 
Chile 
countrycode 
CL 
component 
Revista 
access 
En linea 
databasecode 
revscielocl 
tag 
revista 
region 
America del Sur 
libraryname 
SciELO 
language 
English 
format 
Digital 
author 
Boua,Abdelkarim Ashraf,Mohammad 
spellingShingle 
Boua,Abdelkarim Ashraf,Mohammad Prime rings with involution involving left multipliers 
author_facet 
Boua,Abdelkarim Ashraf,Mohammad 
author_sort 
Boua,Abdelkarim 
title 
Prime rings with involution involving left multipliers 
title_short 
Prime rings with involution involving left multipliers 
title_full 
Prime rings with involution involving left multipliers 
title_fullStr 
Prime rings with involution involving left multipliers 
title_full_unstemmed 
Prime rings with involution involving left multipliers 
title_sort 
prime rings with involution involving left multipliers 
description 
Abstract Let R be a prime ring of characteristic different from 2 with involution ’∗’ of the second kind and n ≥ 1 be a fixed positive integer. In the present paper it is shown that if R admits nonzero left multipliers S and T , then the following conditions are equivalent: (i)R is commutative, (ii) Tn([x, x∗]) ∈ Z(R) for all x ∈ R; (iii) Tn(x ◦ x∗) ∈ Z(R) for all x ∈ R; (iv) [S(x), T (x∗)] ∈ Z(R) for all x ∈ R; (v) [S(x), T (x∗)] − (x ◦ x∗) ∈ Z(R) for all x ∈ R; (vi) S(x) ◦ T (x∗) ∈ Z(R) for all x ∈ R; (vii) S(x) ◦ T (x∗) − [x, x∗] ∈ Z(R) for all x ∈ R. The existence of hypotheses in various theorems have been justified by the examples. 
publisher 
Universidad Católica del Norte, Departamento de Matemáticas 
publishDate 
2020 
url 
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S071609172020000200341 
work_keys_str_mv 
AT bouaabdelkarim primeringswithinvolutioninvolvingleftmultipliers AT ashrafmohammad primeringswithinvolutioninvolvingleftmultipliers 
_version_ 
1755990083855450112 