L. A. Kurdachenko, V. S. Yashchuk, I. Ya. Subbotin, “Lattice groups”, Algebra Discrete Math., 2015, Volume 20, Issue 1,Pages <nobr>126

This article is cited in 1 paper

RESEARCH ARTICLE

Lattice groups

L. A. Kurdachenko^a, V. S. Yashchuk^a, I. Ya. Subbotin^b

^a Department of Algebra, Oles Honchar Dnipropetrovsk National University
^b Department of Mathematics and Natural Sciences, National University

Abstract: In this paper, we introduce some algebraic structure associated with groups and lattices. This structure is a semigroup and it appeared as the result of our new approach to the fuzzy groups and $L$-fuzzy groups where $L$ is a lattice. This approach allows us to employ more convenient language of algebraic structures instead of currently accepted language of functions.

Keywords: group, lattice, distributive lattice, fuzzy group, semigroup.

MSC: 20M10, 06D99, 20M99

Received: 02.04.2015
Revised: 02.04.2015

Language: English