$1$-absorbing prime property in lattices

Document Type : Research Paper

Author

University of Guilan

Abstract

Let $\pounds$ be a bounded distributive lattice. Following the concept of $1$-absorbing prime ideal, we define $1$-absorbing prime filters of $\pounds$. A proper filter $F$ of $\pounds$ is called $1$-absorbing prime filter of $\pounds$ if whenever non-zero elements $a, b, c \in \pounds$ and $a \vee b \vee c \in F$, then either $a \vee b \in F$ or $c \in F$. We will make an intensive investigate the basic properties and possible structures of these filters.

Keywords

Journal of Algebra and Related Topics

Articles in Press, Accepted Manuscript
Available Online from 04 December 2024

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