On Isomorphism Theorems for MI-groups

DOI

10.2991/eusflat.2013.114How to use a DOI?

Keywords

Many identities groups Fuzzy numbers Isomorphism theorems

Abstract

The theory of MI-algebras (``Many Identities''-algebras) has been introduced by M. Holcapek and M. Stepnicka 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.

Copyright

© 2013, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Michal Holcapek
AU  - Michaela Wrublova
AU  - Martin Stepnicka
PY  - 2013/08
DA  - 2013/08
TI  - On Isomorphism Theorems for MI-groups
BT  - Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-13)
PB  - Atlantis Press
SP  - 804
EP  - 811
SN  - 1951-6851
UR  - https://doi.org/10.2991/eusflat.2013.114
DO  - 10.2991/eusflat.2013.114
ID  - Holcapek2013/08
ER  -