Commuting maps on alternative rings

Suppose R is a 2,3-torsion free unital alternative ring having an idempotent element e 1 e 2 = 1 - e 1 which satisfies x R · e i = { 0 } ⇒ x = 0 i = 1 , 2 . In this paper, we aim to characterize the commuting maps. Let φ be a commuting map of R so it is shown that φ ( x ) = z x + Ξ ( x ) for all x ∈...

Full description

Saved in:
Bibliographic Details
Published in:Ricerche di matematica 2022-06, Vol.71 (1), p.67-78
Main Authors: Ferreira, Bruno Leonardo Macedo, Kaygorodov, Ivan
Format: Article
Language:English
Subjects:
Algebra
Analysis
Geometry
Mathematics
Mathematics and Statistics
Numerical Analysis
Probability Theory and Stochastic Processes
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Suppose R is a 2,3-torsion free unital alternative ring having an idempotent element e 1 e 2 = 1 - e 1 which satisfies x R · e i = { 0 } ⇒ x = 0 i = 1 , 2 . In this paper, we aim to characterize the commuting maps. Let φ be a commuting map of R so it is shown that φ ( x ) = z x + Ξ ( x ) for all x ∈ R , where z ∈ Z ( R ) and Ξ is an additive map from R into Z ( R ) . As a consequence a characterization of anti-commuting maps is obtained and we provide as an application, a characterization of commuting maps on von Neumann algebras relative alternative C ∗ -algebra with no central summands of type I 1 .
ISSN:0035-5038
1827-3491
DOI:10.1007/s11587-020-00547-z