Name
Abstract | ||
|---|---|---|
The topic of the paper are Omega-algebras, where Omega is a complete lattice. In this research we deal with congruences and homomorphisms. An Omega-algebra is a classical algebra which is not assumed to satisfy particular identities and it is equipped with an Omega-valued equality instead of the ordinary one. Identities are satisfied as lattice theoretic formulas. We introduce Omega-valued congruences, corresponding quotient Omega-algebras and Omega-homomorphisms and we investigate connections among these notions. We prove that there is an Omega-homomorphism from an Omega-algebra to the corresponding quotient Omega-algebra. The kernel of an Omega-homomorphism is an Omega-valued congruence. When dealing with cut structures, we prove that an Omega-homomorphism determines classical homomorphisms among the corresponding quotient structures over cut subalgebras. In addition, an Omega-congruence determines a closure system of classical congruences on cut sub-algebras. Finally, identities are preserved under Omega-homomorphisms. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.14736/kyb-2017-5-0892 | KYBERNETIKA |
Keywords | Field | DocType |
lattice-valued algebra,congruence,homomorphism | Mathematical optimization,Pure mathematics,Omega,Homomorphism,Congruence relation,Mathematics | Journal |
Volume | Issue | ISSN |
53 | 5 | 0023-5954 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Elijah Eghosa Edeghagba | 1 | 0 | 0.34 |
| Branimir Šešelja | 2 | 170 | 23.33 |
| Andreja Tepavcevic | 3 | 143 | 22.67 |