Authors: Edeghagba, Elijah Eghosa
Šešelja, Branimir
Tepavčević, Andreja 
Title: Congruences and Homomorphisms on Ω -algebras
Journal: Kybernetika
Volume: 53
Issue: 5
First page: 892
Last page: 910
Issue Date: 1-Jan-2017
Rank: M23
ISSN: 0023-5954
DOI: 10.14736/kyb-2017-5-0892
Abstract: 
The topic of the paper are -algebras, where is a complete lattice. In this research we deal with congruences and Ω-homomorphisms. An -algebra is a classical algebra which is not assumed to satisfy particular identities and it is equipped with an -valued equality instead of the ordinary one. Identities are satisfied as lattice theoretic formulas. We introduce -valued congruences, corresponding quotient -algebras and -Ω-homomorphisms and we investigate connections among these notions. We prove that there is an -Ω-homomorphism from an -algebra to the corresponding quotient -algebra. The kernel of an -Ω-homomorphism is an -valued congruence. When dealing with cut structures, we prove that an -Ω-homomorphism determines classical Ω-homomorphisms among the corresponding quotient structures over cut subalgebras. In addition, an -congruence determines a closure system of classical congruences on cut subalgebras. Finally, identities are preserved under -Ω-homomorphisms.
Keywords: Congruence | Homomorphism | Lattice-valued algebra
Publisher: Academy of Sciences of the Czech Republic, Institute of Information Theory and Automation
Project: Development of methods of computation and information processing: theory and applications 

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