| Autor: |
EDEGHAGBA,, ELIJAH EGHOSA, ŠEŠELJA, BRANIMIR, TEPAVČEVIĆ, ANDREJA |
| Předmět: |
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| Zdroj: |
Kybernetika; 2017, Vol. 53 Issue 5, p892-910, 19p, 1 Diagram, 10 Charts |
| Abstrakt: |
The topic of the paper are Ω-algebras, where Ω is a complete lattice. In this research we deal with congruences and homomorphisms. An Ω-algebra is a classical algebra which is not assumed to satisfy particular identities and it is equipped with an Ω-valued equality instead of the ordinary one. Identities are satisfied as lattice theoretic formulas. We introduce Ω-valued congruences, corresponding quotient Ω-algebras and Ω-homomorphisms and we investigate connections among these notions. We prove that there is an Ω-homomorphism from an Ω-algebra to the corresponding quotient Ω-algebra. The kernel of an Ω-homomorphism is an Ω-valued congruence. When dealing with cut structures, we prove that an Ω-homomorphism determines classical homomorphisms among the corresponding quotient structures over cut subalgebras. In addition, an Ω-congruence determines a closure system of classical congruences on cut subalgebras. Finally, identities are preserved under Ω-homomorphisms. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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