Journal of the
Korean Mathematical Society JKMS

As a continuation of the paper [3], in this paper we investigate the further properties on $LI$-ideals, and show that how to generate an $LI$-ideal by both an $LI$-ideal and an element. We define a prime $LI$-ideal, and give an equivalent condition for a proper $LI$-ideal to be prime. Using this result, we establish the extension property and prime $LI$-ideal theorem.

Keywords: lattice (H) implication algebra, $LI$-ideal, lattice ideal, prime $LI$-ideal

MSC numbers: 03G10, 06B10, 54E15