mp-residuated lattices

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RASOULI SAEED; HEIDARI DARIUSH

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ISSN: 2588-4824

Journal Paper

Paper Information

Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2021 | Volume:7 | Issue:29 Page(s): 29-42

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Information Journal Paper

Title

mp-residuated lattices

Author(s)

RASOULI SAEED | HEIDARI DARIUSH | Issue Writer Certificate

Keywords

residuated lattice

minimal prime filter

mp-residuated lattice

ω-filter

divisor filter

Abstract

In this paper, the notion of mp-residuated lattice, as a subclass of residuated lattices in which every prime filter contains a unique minimal prime filter, is introduced and investigated. For a residuated lattice A, the notion of ω-filter is introduced and it is shown that Ω (A), the set of ω-filters of A, is a bounded distributive lattice. Also, it is observed that γ (A), the set of coannulets of A, is a sublattice of Ω (A). Then for each prime filter P of A, the notion of the divisor filter D(P) as an important tool in investigating of minimal prime filters of A is introduced and it is proved that a prime filter P is minimal prime if and only if P=D(P). Finally, by the notion of ω-filters, as an extension of divisor filters, a fundamental characterization of mp-residuated lattices is given and it is shown that a residuated lattice is mp if and only if the set of its ω-filters is a sublattice of the lattice of its filters.

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APA: Copy

RASOULI, SAEED, & HEIDARI, DARIUSH. (2021). mp-residuated lattices. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 7(29 ), 29-42. SID. https://sid.ir/paper/969234/en

Vancouver: Copy

RASOULI SAEED, HEIDARI DARIUSH. mp-residuated lattices. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2021;7(29 ):29-42. Available from: https://sid.ir/paper/969234/en

IEEE: Copy

SAEED RASOULI, and DARIUSH HEIDARI, “mp-residuated lattices,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 7, no. 29 , pp. 29–42, 2021, [Online]. Available: https://sid.ir/paper/969234/en

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