<abstract xmlns="http://www.w3.org/1999/xhtml">In this note, we introduce the notion of n × m-ideal on n × m- valued Łukasiewicz-Moisil algebras (or LMn×m-algebras) which allows us to consider a topology on them. Besides, we define the concept of F-multiplier, where F is a topology on an LMn×m-algebra L, which is used to construct the localization LMn×m-algebra LF. Furthermore, we prove that the LMn×m-algebra of fractions LS associated with an ⋀-closed subset S of L is an LMn×m-algebra of localization. Finally, in the finite case we prove that LS is isomorphic to a special subalgebra of L. Since n-valued Łukasiewicz-Moisil algebras are a particular case of LMn×m-algebras, all these results generalize those obtained in [4] (see also [3]).</abstract>

In this note, we introduce the notion of n × m-ideal on n × m- valued Łukasiewicz-Moisil algebras (or LMn×m-algebras) which allows us to consider a topology on them. Besides, we define the concept of F-multiplier, where F is a topology on an LMn×m-algebra L, which is used to construct the localization LMn×m-algebra LF. Furthermore, we prove that the LMn×m-algebra of fractions LS associated with an ⋀-closed subset S of L is an LMn×m-algebra of localization. Finally, in the finite case we prove that LS is isomorphic to a special subalgebra of L. Since n-valued Łukasiewicz-Moisil algebras are a particular case of LMn×m-algebras, all these results generalize those obtained in [4] (see also [3]).

F–multipliers and the localization of LMn×m–algebras

Departamento de Matemática, Universidad Nacional del Sur, Avenida Alem 1253, 8000 Bah´ıa Blanca, Argentina

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

{"article-title":"F\u2013multipliers and the localization of LMn×m\u2013algebras"}

In this note, we introduce the notion of n × m-ideal on n × m- valued Łukasiewicz-Moisil algebras (or LMn×m-algebras) which allows us to consider a topology on...

F–multipliers and the localization of LMn×m–algebras

Published Online: Jul 30, 2013

Page range: 285 - 304

DOI: https://doi.org/10.2478/auom-2013-0019

This content is open access.