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 a...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Boua,Abdelkarim, Ashraf,Mohammad
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2020
Materias:	Prime ring Derivation Multiplier Involution Commutativity
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000200341
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:scielo:S0716-09172020000200341
record_format	dspace
spelling	oai:scielo:S0716-091720200002003412020-05-06Prime 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:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.39 n.2 20202020-04-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000200341en10.22199/issn.0717-6279-2020-02-0021
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Prime ring Derivation Multiplier Involution Commutativity
spellingShingle	Prime ring Derivation Multiplier Involution Commutativity Boua,Abdelkarim Ashraf,Mohammad 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.
author	Boua,Abdelkarim Ashraf,Mohammad
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
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2020
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000200341
work_keys_str_mv	AT bouaabdelkarim primeringswithinvolutioninvolvingleftmultipliers AT ashrafmohammad primeringswithinvolutioninvolvingleftmultipliers
_version_	1718439868487434240

Prime rings with involution involving left multipliers

Ejemplares similares