On S-J-filters of a bounded lattice
Shahabaddin Ebrahimi Atani
Department of Pure Mathematics, Guilan University, Rasht, Iran.
Pages 113-125 | Received 10 June 2025, Accepted 03 September 2025, Published 19 July 2026
Abstract
Let \mathcal{L} be a bounded lattice and S denote the join subset of \mathcal{L}. In this paper, we introduce the concept of S\text{-}J-filters as a new generalization of J-filters. Many of the basic properties and characterizations of this concept are investigated. We study S\text{-}J-filters under various contexts of constructions such as the stability of S\text{-}J-join subsets in some lattice-theoretic constructions, homomorphic image lattices, quotient lattices, cartesian product lattices, S finite filters, SJ-finite filters, SJ Noetherian lattices and filterlization lattices.
Keywords: lattice, J-filter, S\text{-}J-filter.
MSC numbers: Primary: 06B15, 06B20; Secondary 05C25, 05C40.
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