Let R be a commutative ring with nonzero identity and, S⊆ R be a multiplicatively closed
subset. An ideal P of R with P∩ S=∅ is called an S-prime ideal if there exists an (fixed) s∈ S …

In this paper, new criteria for zero dimensional rings, Gelfand rings, clean rings and mp-rings
are given. A new class of rings is introduced and studied, we call them purified rings …

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 …

In this paper, new algebraic and topological results on purely-prime ideals of a commutative
ring (pure spectrum) are obtained. Particularly, Grothendieck-type theorem is obtained …

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 …

In this paper, it is shown that the Boolean ring of a commutative ring is isomorphic to the ring
of clopens of its prime spectrum. In particular, Stone's Representation Theorem is …

arXiv:1708.03199v5 [math.AC] 28 Jan 2020 Page 1 arXiv:1708.03199v5 [math.AC] 28 Jan
2020 ZARISKI COMPACTNESS OF MINIMAL SPECTRUM AND FLAT COMPACTNESS OF …

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 …

Let R be a commutative ring with nonzero identity and M be an R-module. In this paper, first
we give some relations between S-prime and S-maximal submodules that are …