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 …

Several topologies can be defined on the prime, the maximal and the minimal prime spectra
of a commutative ring; among them, we mention the Zariski topology, the patch topology and …

It is known that by using the commutator operation, for each congruence modular algebra $
A $ one can define a notion of prime congruence. The set $ Spec (A) $ of prime …

We know from a previous paper that the reticulation of a coherent quantale A is a bounded
distributive lattice L (A) whose prime spectrum is homeomorphic to m-prime spectrum of A …

In this paper, using the canonical correspondence between the idempotents and clopens,
we obtain several new results on lifting idempotents. The Zariski clopens of the maximal …

Let R be a commutative ring with the unit element. It is shown that an ideal I in R is pure if
and only if Ann (f)+ I= R for all f∈ I. If J is the trace of a projective R-module M, we prove that …

This paper studies a fascinating type of filter in residuated lattices, the so-called pure filters.
A combination of algebraic and topological methods on the pure filters of a residuated lattice …

In this study, we define a new concept, ie, source of primeness of a ring $ R $, as $ P_
{R}:=\bigcap_ {a\in R} S_ {R}^{a} $ such that $ S_ {R}^{a}:=\{b\in R\mid aRb=(0)\} $. We then …

This paper is devoted to the study of a fascinating class of residuated lattices, the so-called
mp-residuated lattice, in which any prime filter contains a unique minimal prime filter. A …

In this paper, we consider the N-pure notion. An ideal $ I $ of a ring $ R $ is said to be N-
pure, if for every $ a\in I $ there exists $ b\in I $ such that $ a (1-b)\in N (R) $, where N (R) is …