Journal of Algebra, Number Theory: Advances and ApplicationsAuthor's: Albert Kadji and Marcel Tonga
Pages: [65] - [94]
Received Date: May 9, 2015; Revised July 21, 2015
Submitted by:
DOI: http://dx.doi.org/10.18642/jantaa_7100121495
We study the notion of semi-maximal filter, and establish some relationships with and other types of filters in residuated lattice. We give a suitable sufficient condition under which an n-fold Boolean filter is semi-maximal and then, we give an answer to an open problem from [2]. In addition, the notions of n-fold peculiar (resp., perfect, semi-Boolean, strong, strongly integral) filters are given and we use them to characterize the notions of n-fold bipartite (resp., peculiar, perfect, semi-Boolean, strong, strongly integral) residuated lattices. We observe that a residuated lattice is n-fold bipartite iff it has an n-fold Boolean filter. The class of n-fold strong (resp., strongly integral) residuated lattices is a subvariety of the variety of all residuated lattices; and we see that an n-fold strong residuated lattice is a new generalization of MV-algebra. At the end of the paper, we draw the diagram summarizing the relations between different types of residuated lattices.
semi-maximal filter, semi-locally finite residuated lattice, n-fold strong (resp., strongly integral) residuated lattice.
