International Journal of Science, Engineering and TechnologyAuthors: P. Ramulu, J. Niranjana Goud
Abstract: BCI-algebras constitute an important class of algebraic structures arising from non-classical logic and implicational systems. They generalize BCK-algebras and play a significant role in the study of algebraic logic, order theory, and abstract algebraic systems. In this paper, we introduce and investigate a special class of BCI-algebras characterized by the non-existence of singular elements. An element of a BCI-algebra is said to be singular if it satisfies certain restrictive operational conditions that lead to structural degeneracy. By eliminating such elements, we obtain a refined algebraic framework that preserves the core axioms of BCI-algebras while ensuring improved structural regularity.We establish fundamental properties of non-singular BCI-algebras and examine their relationships with ideals, sub algebras, and holomorphic images. Several equivalent conditions characterizing the absence of singular elements are derived. Furthermore, we study the behaviour of these algebras under standard constructions and provide illustrative examples to distinguish them from general BCI-algebras. It is shown that every non-singular BCI-algebra exhibits enhanced cancellation-like properties and stronger order-theoretic behaviour.The results contribute to a deeper structural understanding of BCI-algebras and suggest potential applications in classification theory and logical algebraic modelling.
DOI: https://doi.org/10.5281/zenodo.19441040
