All the cardinal numbers of ideals G-part of Q-algebras

Koppitz, Jörg; Anantayasethi, Ananya

doi:10.47974/JDMSC-2609

Open Access Research Article

All the cardinal numbers of ideals G-part of Q-algebras

Jörg Koppitzkoppitz@math.bas.bgInstitute of Mathematics and InformaticsBulgarian Academy of SciencesSofia, 14476, BulgariaView full profile → , ^*Ananya AnantayasethiCorresponding authorananya.a@msu.ac.thAlgebra and Application Research UnitMahasarakham UniversityMahasarakham, 44150, ThailandView full profile →

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pp. 363–373Vol. 29Issue 1January 2026DOI: 10.47974/JDMSC-2609 Crossmark XML

Received:: 07 May 2025
Published Online:: 15 Jan 2026
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-2609
Pages:: 363–373

Abstract

A Q-algebra (ξ; *, 0) is a generalization of the concepts of BCK, BCI-algebras, introduced by Neggers et al. [1]. As for BCK, BCI-algebras, the concept ideal is defined for Q-algebras [1]. In this paper, we show that for a given integer n, and for all k ∈ {0, 1, …, log2n – 1}, there is a Q-algebra ξ of cardinality n such that the G-part G(ξ) = {υ ∈ ξ : 0 * υ = υ} is an ideal of ξ with |G(ξ)|= 2k. Moreover, we show that if G(ξ) is an ideal of a Q-algebra ξ and |ξ|= n, then |G(ξ)|= 2k, for some k ∈ {0, 1, 2, …, log2 n – 1}.

Keywords

Q-algebra Ideals G-part Cardinality Abelian group

Subject Classifications

Primary 03G2503G2706F3520K01

References

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