ON 2-ABSORBING FILTERS OF LATTICES
Journal Title: Discussiones Mathematicae - General Algebra and Applications - Year 2016, Vol 36, Issue 2
Abstract
Let L be a lattice with 1. In this paper we study the concept of 2-absorbing filter which is a generalization of prime filter. A proper filter F of L is called a 2-absorbing filter (resp. a weakly 2-absorbing) if whenever x1 ∨ x2 ∨ x3 ∈ F (resp. 1 6= x1 ∨ x2 ∨ x3 ∈ F), for x1, x2, x3 ∈ L, then there are 2 of the xi’s whose join is in F. A basic number of results concerning 2-absorbing filters and weakly of 2-absorbing filters are given in the case when L is distributive.
Authors and Affiliations
S. Ebrahimi Atani, M. Sedghi Shanbeh Bazari
Keywords
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