Rickart residuated lattices, By Saeed Rasoli

Research

Title	Rickart residuated lattices
Type	Article
Keywords	Rickart residuated lattice, Baer residuated lattice, Quasicomplemented residuated lattice, Normal residuated lattice, Generalized stone residuated lattice
Journal	SOFT COMPUTING
DOI	https://doi.org/10.1007/s00500-021-06227-w
Researchers	Saeed Rasoli (First researcher)

Abstract

In this paper, the notion of a Rickart residuated lattice is introduced and investigated. A residuated lattice is called Rickart if any its coannulet is generated by a complemented element. It is observed that a residuated lattice A, is Rickart iff any its coannulet is a direct summand of A iff it is quasicomplemented and normal iff it is generalized Stone. Some algebraic and topological characterizations are obtained, and some facts about pure and Stone filters are also extracted, which are given in the paper.