Abstract
AbstractIn this paper, the notions of maximal GE-filter and prime GE-filter of a GE-algebra are introduced and the relation between them is given. Some characterizations of prime GE-filters of a transitive GE-algebra are given in terms of the GE-filter generated by a subset of a transitive GE-algebra. We generalized Stone’s theorem to transitive GE-algebras. The notion of elitable GE-filter of a bordered GE-algebra is introduced and investigated its properties. We observed that the class of all elitable GE-filters of a transitive bordered GE-algebra is a complete distributive lattice. Equivalent conditions for a GE-filter of a transitive bordered GE-algebra to be elitable GE-filter are given. We provided conditions for a subset of a transitive bordered GE-algebra to be elitable GE-filter.
Publisher
Springer Science and Business Media LLC
Subject
Geometry and Topology,Theoretical Computer Science,Software
Reference16 articles.
1. Bandaru RK, Borumand Saeid A, Jun YB (2021) On GE-algebras. Bull Sect Logic 50(1):81–96. https://doi.org/10.18778/0138-0680.2020.20
2. Bandaru RK, Öztürk MA, Jun YB (2021) Bordered GE-algebras, J Algeraic Syst (submitted)
3. Celani S (2002) A note on homomorphisms of Hilbert algebras. Int J Math Math Sci 29(1):55–61. https://doi.org/10.1155/S0161171202011134
4. Chajda I, Halas R, Jun YB (2002) Annihilators and deductive systems in commutative Hilbert algebras. Comment Math Univ Carol 43(3):407–417
5. Diego A (1966) Sur les algebres de Hilbert. Collection de Logique Mathematique, Edition Hermann, Serie A, XXI