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arXiv · 2405.11670

On $z$-elements of multiplicative lattices

Themba Dube·Amartya Goswami
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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.

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Themba Dube, Amartya Goswami. 2024-05-19. On $z$-elements of multiplicative lattices. https://arxiv.org/abs/2405.11670

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