Some properties of 2-absorbing primary ideals in lattices

Abstract

We introduce the concepts of a primary and a 2-absorbing primary ideal and the radical of an ideal in a lattice. We study some properties of these ideals. A characterization for the radical of an ideal to be a primary ideal is given. Also a characterization for an ideal I to be a 2-absorbing primary ideal is proved. Examples and counter examples are given wherever necessary. Keywords: Ideal, Prime ideal, Primary ideal, 2-absorbing ideal, 2-absorbing primary ideal