Characterization of ideals of Q-algebras related to its G-part

Anantayasethi, Ananya; Koppitz, Jörg

doi:10.47974/JDMSC-2071

Open Access Research Article

Characterization of ideals of Q-algebras related to its G-part

Ananya Anantayasethiananya.a@msu.ac.thAlgebra and Applications Research UnitMahasarakham UniversityMahasakham, 44150, ThailandView full profile → , ^*Jörg KoppitzCorresponding authorkoppitz@math.bas.bgInstitute of Mathematics and InformaticsBulgarian Academy of SciencesSofia, 14476, BulgariaView full profile →

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pp. 131–141Vol. 28Issue 1February 2025DOI: 10.47974/JDMSC-2071 Crossmark XML

Received:: 03 Dec 2024
Published Online:: 28 Feb 2025
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-2071
Pages:: 131–141

Abstract

In this work, we study the G-part of Q-algebras A, i.e. the set G(A) = {w ∈ A | 0w = w}. We show that G(A) is an abelian group, whenever G(A) is an ideal and characterize all Q-algebras A such that G(A) is an ideal of A. Moreover, we show that, up to isomorphism, there is only one Q-algebra A with G(A) = A, which is only possible if |A| = 2k (k ∈ ℕ).

Keywords

Q-algebra Ideals G-part Abelian group Homomorphism

Subject Classifications

03G2503G2706F3520K01

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