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Shahabaddin Ebrahimi Atani
Department of Mathematics, University of Guilan P. O. Box 1914 Rasht Iran
Mathematics

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On Weakly S-Prime Elements of Lattices Shahabaddin Ebrahimi Atani
Journal of the Indonesian Mathematical Society VOLUME 30 NUMBER 1 (MARCH 2024)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.30.1.1604.89-99

Abstract

Let £ be a bounded distributive lattice and S a join-subset of £. In this paper, we introduce the concept of S-prime elements (resp. weakly S-prime elements) of £. Let p be an element of £ with S ∧p = 0 (i.e. s∧p = 0 for all s ∈ S). We say that p is an S-prime element (resp. a weakly S-prime element) of £ if there is an element s ∈ S such that for all x, y ∈ £ if p ≤ x ∨ y (resp. p ≤ x ∨ y 6= 1), then p ≤ x ∨ s or p ≤ y ∨ s. We extend the notion of S-prime property in commutative rings to S-prime property in lattices.
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