2018/12/30 by Rasouli, Saeed, Kondo, Michiro
#FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1812.11511
The notion of n-normal residuated lattice, as a class of residuated lattices in which every prime filter contains at most n minimal prime filters, is introduced and studied. Before that, the notion of ω-filter is introduced and it is observed that the set of ω-filters in a residuated lattice forms a distributive lattice on its own, which includes the set of coannulets as a sublattice. The class of n-normal residuated lattices is characterized in terms of their prime filters, minimal prime filters, coannulets and ω-filters.