<abstract xmlns="http://www.w3.org/1999/xhtml">

The aim of this article is to introduce the concept of centrally-extended Jordan epimorphisms and proving that if <italic>R</italic> is a non-commutative prime ring (∗-ring) of characteristic not two, and <italic>G</italic> is a CE-Jordan epimorphism such that [<italic>G</italic>(<italic>x</italic>), <italic>x</italic>] ∈ <italic>Z</italic>(<italic>R</italic>) ([<italic>G</italic>(<italic>x</italic>), <italic>x</italic>∗] ∈ <italic>Z</italic>(<italic>R</italic>)) for all <italic>x</italic> ∈ <italic>R</italic>, then <italic>R</italic> is an order in a central simple algebra of dimension at most 4 over its center or there is an element <italic>λ</italic> in the extended centroid of <italic>R</italic> such that <italic>G</italic>(<italic>x</italic>) = <italic>λx</italic> (<italic>G</italic>(<italic>x</italic>) = <italic>λx</italic>∗) for all <italic>x</italic> ∈ <italic>R</italic>.
</abstract>

The aim of this article is to introduce the concept of centrally-extended Jordan epimorphisms and proving that if R is a non-commutative prime ring (∗-ring) of characteristic not two, and G is a CE-Jordan epimorphism such that [G(x), x] ∈ Z(R) ([G(x), x∗] ∈ Z(R)) for all x ∈ R, then R is an order in a central simple algebra of dimension at most 4 over its center or there is an element λ in the extended centroid of R such that G(x) = λx (G(x) = λx∗) for all x ∈ R.

Rings with centrally-extended Jordan epimorphisms

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

{"article-title":"Rings with centrally-extended Jordan epimorphisms"}

The aim of this article is to introduce the concept of centrally-extended Jordan epimorphisms and proving that if R is a non-commutative prime ring (∗-ring) of...

Rings with centrally-extended Jordan epimorphisms

Published Online: Mar 28, 2024

Page range: 19 - 27

Received: Oct 12, 2023

Accepted: Jan 09, 2024

DOI: https://doi.org/10.2478/aupcsm-2024-0003

Keywords
derivations, centrally-extended derivations, endomorphisms, centrally-extended endomorphisms, centrally-extended Jordan endomorphisms, prime rings

© 2024 Aziza Gouda et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

Rings with centrally-extended Jordan epimorphisms

Published Online: Mar 28, 2024

Page range: 19 - 27

Received: Oct 12, 2023

Accepted: Jan 09, 2024

DOI: https://doi.org/10.2478/aupcsm-2024-0003

Keywordsderivations, centrally-extended derivations, endomorphisms, centrally-extended endomorphisms, centrally-extended Jordan endomorphisms, prime rings

© 2024 Aziza Gouda et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

Keywords
derivations, centrally-extended derivations, endomorphisms, centrally-extended endomorphisms, centrally-extended Jordan endomorphisms, prime rings