International Journal of Technology and Applied Science

E-ISSN: 2230-9004   •   Impact Factor: 10.31

A Widely Indexed Open Access Peer Reviewed Multidisciplinary Bi-monthly Scholarly International Journal

Call for Paper Volume 17 Issue 3 (March 2026) Submit your research before the last 3 days of this month to publish your research paper in the current issue.
Submit Research Paper Join as a Reviewer

Plagiarism is checked by the leading plagiarism checker TurnItIn

Call for Paper

Volume 17 Issue 3
March 2026

Submit your research paper

Indexing Partners
Academia Advanced Sciences Index Bielefeld Academic Search Engine CiteSeer DRJI Google Scholar Independent Search Engine & Directory Network ISI (International Scientific Indexing) Issuu Mendeley Research Networks
RefSeek ResearcherId - Thomson Reuters ResearchGate Scirus Scribd Semantic Scholar UTeM - Universiti Teknikal Malaysia Melaka Wiki for Call for Papers WorldCat Zenodo

Generalized Derivations on Unital Prime Banach Algebras with Nontrivial Center: Structural Properties and Commutativity Theorems

Author(s) Dr. S. Lalitha
Country India
Abstract This paper investigates the structural behavior of generalized derivations defined on unital prime Banach algebras whose centers are nontrivial. Generalized derivations, which extend the classical notion of derivations by incorporating an additive mapping alongside a standard derivation, have gained significant attention in functional analysis and ring theory due to their rich algebraic structure and implications for commutativity. In the setting of unital prime Banach algebras, the existence of a nontrivial center introduces additional constraints that profoundly influence the behavior of such mappings. We establish several structural properties of generalized derivations under various functional identities and polynomial constraints. In particular, we prove that if a generalized derivation F associated with a derivation d satisfies certain central-valued conditions on a prime Banach algebra A, then both F and d must exhibit specific commutativity-forcing behaviors. A series of commutativity theorems are derived, demonstrating that the algebra A is necessarily commutative under prescribed conditions involving the action of F on the center or on Lie ideals of A. Our results generalize and extend several known theorems in the literature on prime rings and Banach algebras. Applications to automatic continuity and the Singer–Wermer conjecture are also discussed.
Keywords Generalized derivations, prime Banach algebras, commutativity theorems, nontrivial center, functional identities, Lie ideals, automatic continuity, Singer–Wermer conjecture.
Published In Volume 17, Issue 3, Array 2026
Published On 2026-03-09
Cite This Generalized Derivations on Unital Prime Banach Algebras with Nontrivial Center: Structural Properties and Commutativity Theorems - Dr. S. Lalitha - IJTAS Volume 17, Issue 3, Array 2026.
View / Download PDF File

Share this



CrossRef

CrossRef DOI is assigned to each research paper published in our journal.

IJTAS DOI prefix is
10.71097/IJTAS

Downloads
Research Paper Format Copyright Permission Form and Undertaking Form Cover Page Vol 15 Isu 12Cover Page Vol 15 Isu 11Cover Page Vol 15 Isu 10

All research papers published on this website are licensed under Creative Commons Attribution-ShareAlike 4.0 International License, and all rights belong to their respective authors/researchers.

CC-BY-SA Open Access

About IJTAS
Fees & Payment
Current Issue
Publication Archive 		Submit Research Paper
Track Submission Status
Publication Guidelines
Publication Ethics
Peer Review & Plagiarism 		Join as a Reviewer
Editors & Reviewers
Reviewer Referral Program
Get Reviewer Membership Certi. 		Website/Journal Policies
Usage Policy
Content Policies
Privacy Policy
Contact Us Message on WhatsApp +91-9687-182-185 editor@ijtas.com