On z-elements of multiplicative lattices

Amartya Goswami; Themba Dube

doi:10.1007/s00012-024-00882-4

On z-elements of multiplicative lattices

Amartya Goswami, Themba Dube

Mathematics and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The aim of this paper is to investigate further properties of z-elements in multiplicative lattices. We utilize z-closure operators to extend several properties of z-ideals to z-elements and introduce various distinguished subclasses of z-elements, such as z-prime, z-semiprime, z-primary, z-irreducible, and z-strongly irreducible elements, and study their properties. We provide a characterization of multiplicative lattices where z-elements are closed under finite products and a representation of z-elements in terms of z-irreducible elements in z-Noetherian multiplicative lattices.

Original language	English
Article number	4
Journal	Algebra Universalis
Volume	86
Issue number	1
DOIs	https://doi.org/10.1007/s00012-024-00882-4
Publication status	Published - Feb 2025

Keywords

Multiplicative lattice
Prime element
Strongly irreducible element
z-element

ASJC Scopus subject areas

Algebra and Number Theory
Logic

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10.1007/s00012-024-00882-4

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AB - The aim of this paper is to investigate further properties of z-elements in multiplicative lattices. We utilize z-closure operators to extend several properties of z-ideals to z-elements and introduce various distinguished subclasses of z-elements, such as z-prime, z-semiprime, z-primary, z-irreducible, and z-strongly irreducible elements, and study their properties. We provide a characterization of multiplicative lattices where z-elements are closed under finite products and a representation of z-elements in terms of z-irreducible elements in z-Noetherian multiplicative lattices.

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KW - Strongly irreducible element

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On z-elements of multiplicative lattices

Abstract

Keywords

ASJC Scopus subject areas

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