2019/04/20 by Rasouli, Saeed
#06D20 #06F99 #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1904.10302
In this paper, the class of quasicomplemented residuated lattices is introduced and investigated, as a subclass of residuated lattices in which any prime filter not containing any dense element is a minimal prime filter. The notion of disjunctive residuated lattices is introduced and it is observed that a residuated lattice is Boolean if and only if it is disjunctive and quasicomplemented. Finally, some characterizations for quasicomplemented residuated lattices are given by means of the new notion of α-filters.