Quotient MI-groups

Abstract

A many identities group (MI-group, for short) is a special algebraic structure in which identity like elements (called pseudoidentities) are specified and collected into a monoidal substructure. In this way, many algebraic structures, such as monoids of fuzzy intervals (numbers) or convex bodies possessing behavior very similar to that of a group structure, may be well described and investigated using a new approach, which seems to be superfluous for the classical structures. The concept of MI-groups was recently introduced by Holčapek and Štěpnička in the paper “MI-algebras: A new framework for arithmetics of (extensional) fuzzy numbers” to demonstrate how a standard structure can be generalized in terms of MI-algebras. This paper is a continuation of the development of MI-group theory and is focused on the construction of quotient MI-groups and a specification of the conditions under which the isomorphism theorems for groups are fulfilled for MI-groups.