Congruency, Homomorphism and Isomorphism on Autometrized Algebras.

This paper presents a study of congruence relations on autometrized algebras. We demonstrate that in a normal autometrized algebra, which satisfies certain conditions, the set of all congruence relations forms a complete sublattice within the set of all equivalence relations. Furthermore, we investigate the property that a congruence-permutable autometrized algebra is also congruence-modular. We also explore several fundamental properties related to congruence relations. Additionally, we introduce the kernel of a homomorphism and establish that it is a congruence relation. Lastly, we examine the homomorphism, isomorphism, and correspondence theorems of autometrized algebra using the concept of congruence.