Primary Ideals of Lie Algebras

Abstract

In this paper, we introduce and advance the basic theory of primary ideals for Lie algebras and investigate their properties in details illustrated by several examples. We give some characterizations for ideals to be primary ideals. We also introduce the concept of strongly irreducible ideals. We study the interrelations among primary, prime, semi-prime, strongly ir- reducible, irreducible and maximal ideals in Lie algebra. We show that the maximal ideal is primary ideal. We also show that the concepts of strongly irreducible, primary and prime ideals are all equivalent for prime radical ideals.