$1$-absorbing prime property in lattices

$1$ -absorbing prime property in lattices

Articles in Press

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

\pounds

is called

1

-absorbing prime filter of

\pounds

if whenever non-zero elements

a, b, c \in \pounds

and

a \lor b \lor c \in F

, then either

a \lor b \in F

c \in F

. We will make an intensive investigate the basic properties and possible structures of these filters.

Keywords