many identities groups; algebraic structures; fuzzy numbers; isomorphism theorems

The theory of MI-algebras (Many Identities- algebras) has been introduced by M. Holcapek and M. Štepnicka recently. These structures motivated by an algebraic formalizations of distinct arithmetics of fuzzy numbers, generalize the standard structures (monoids, groups, fields etc.) by employing a whole set of identity-like elements called pseudoidentitites. This leads to natural questions which properties of classical algebraic structures related to arithmetics of crisp numbers are preserved also in the case of MI-structures. This paper focuses on MI-groups, particularly on the properties of their homomorphisms. We show that three crucial theorems of isomorphism that are valid in the classical case, are under some conditions also valid in the theory of MI-groups.