<abstract xmlns="http://www.w3.org/1999/xhtml"> The main aim of this manuscript is to prove the following result. Let n > 2 be a fixed integer and R be a k-torsion free semiprime ring with identity, where k ∈ {2, n - 1, n}. Let us assume that for the additive mapping T : R→ R 3T(xn) = T(x)xn-1+ xT(xn-2)x + xn-1T(x), x ∈R, is also fulfilled. Then T is a two-sided centralizer.</abstract>

The main aim of this manuscript is to prove the following result. Let n > 2 be a fixed integer and R be a k-torsion free semiprime ring with identity, where k ∈ {2, n - 1, n}. Let us assume that for the additive mapping T : R→ R 3T(xn) = T(x)xn-1+ xT(xn-2)x + xn-1T(x), x ∈R, is also fulfilled. Then T is a two-sided centralizer.

On a Functional Equation Related to Two-Sided Centralizers

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"On a Functional Equation Related to Two-Sided Centralizers"}

The main aim of this manuscript is to prove the following result. Let n > 2 be a fixed integer and R be a k-torsion free semiprime ring with identity, where k...

On a Functional Equation Related to Two-Sided Centralizers

Published Online: Aug 24, 2018

Page range: 227 - 235

Received: Mar 22, 2017

Accepted: Sep 21, 2017

DOI: https://doi.org/10.1515/amsil-2017-0014

Keywords
prime ring, semiprime ring, Banach space, standard operator algebra, left (right) centralizer, left (right) Jordan centralizer, two-sided centralizer

© 2018 Irena Kosi-Ulbl, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

On a Functional Equation Related to Two-Sided Centralizers

Published Online: Aug 24, 2018

Page range: 227 - 235

Received: Mar 22, 2017

Accepted: Sep 21, 2017

DOI: https://doi.org/10.1515/amsil-2017-0014

Keywordsprime ring, semiprime ring, Banach space, standard operator algebra, left (right) centralizer, left (right) Jordan centralizer, two-sided centralizer

© 2018 Irena Kosi-Ulbl, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
prime ring, semiprime ring, Banach space, standard operator algebra, left (right) centralizer, left (right) Jordan centralizer, two-sided centralizer