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Shahabaddin Ebrahimi Atani, J-filters of bounded lattices, Eur. J. Math. Appl. 4 (2024), Article ID 12.

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Volume 4 (2024), Article ID 12

https://doi.org/10.28919/ejma.2024.4.12

Published: 10/05/2024

Abstract:

Let $\mathcal{L}$ be a bounded distributive lattice and $J(\mathcal{L})$ denote the Jacobson radical of $\mathcal{L}$. Similar to the definition of $J$-ideals of commutative rings, we introduce and study $J$-filters of lattices. A proper filter $F$ of $\mathcal{L}$ is called a $J$-filter if whenever $x \vee y \in F$ with $x \notin J(\mathcal{L})$, then $y \in F$ for every $x, y \in \mathcal{L}$. The main purpose of this paper is devoted to extend the notion of $J$-ideal property in commutative rings to $J$-filter property in lattices.

How to Cite:

Shahabaddin Ebrahimi Atani, J-filters of bounded lattices, Eur. J. Math. Appl. 4 (2024), Article ID 12. https://doi.org/10.28919/ejma.2024.4.12