Search

Start Over Subject isomorphic refinements

1. Lexicographic product decompositions of half linearly ordered loops

Creator:
Demko, Milan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
half linearly ordered quasigroup, half linearly ordered loop, lexicographic product, and isomorphic refinements
Language:
English
Description:
In this paper we prove for an hl-loop $Q$ an assertion analogous to the result of Jakubík concerning lexicographic products of half linearly ordered groups. We found conditions under which any two lexicographic product decompositions of an hl-loop $Q$ with a finite number of lexicographic factors have isomorphic refinements.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Lexicographic products of half linearly ordered groups

Creator:
Jakubík, Ján
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
half linearly ordered group, lexicographic product, and isomorphic refinements
Language:
English
Description:
The notion of the half linearly ordered group (and, more generally, of the half lattice ordered group) was introduced by Giraudet and Lucas [2]. In the present paper we define the lexicographic product of half linearly ordered groups. This definition includes as a particular case the lexicographic product of linearly ordered groups. We investigate the problem of the existence of isomorphic refinements of two lexicographic product decompositions of a half linearly ordered group. The analogous problem for linearly ordered groups was dealt with by Maltsev [5]; his result was generalized by Fuchs [1] and the author [3]. The isomorphic refinements of small direct product decompositions of half lattice ordered groups were studied in [4].
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public