All the cardinal numbers of ideals G-part of Q-algebras
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}.
Fields of Study & Subjects
Advanced Algebra and Logic
Fuzzy and Soft Set Theory
Advanced Topology and Set Theory
Publication details
- Journal / source
- Journal of Discrete Mathematical Sciences and Cryptography
- Volume
- 29
- Issue
- 1
- Pages
- 363–373
- Publication date
- 1 January 2026