The α -ideals of co-residuated lattices
Abstract
A co-residuated lattice is a logical algebra of non-classical logic systems, built upon the connectives “and not” and “or”. Ideals of co-residuated lattices are not only special subalgebraic structures, but also serve as logical deductive systems. This paper focuses on a particular class of ideals, called the α-ideals, which is closely related to annihilators. It is shown that every minimal α-ideal can induce a closure operator on the set of ideals, with the fixed points being precisely the prime α-ideals. Furthermore, the prime α-ideal topological space is defined and its properties related to bases, compact subsets, T1,T2-separation axioms are investigated.
Fields of Study & Subjects
Rings
Modules
and Algebras
Advanced Algebra and Logic
Commutative Algebra and Its Applications
Publication details
- Journal / source
- Communications in Algebra
- Volume
- 54
- Issue
- 9
- Pages
- 3145–3157
- Publication date
- 5 January 2026
- Language
- EN