Pure Spectrum of an Ag-groupoid with Left Identity and Zero

In this paper S will denote an AG-groupoid. A two-sided ideal I of S is called a right (left) pure ideal of S , if for each x in I , there is an element y in I such that ) = ( = x yx x xy . A left (right) pure ideal I is called purely prime if it is proper and if for any pure ideals 1 I and 2 I : I I I 2 1 implies I I1 or I I2 . Analogous to the construction of the pure spectrum of a semigroup developed in [1], we will construct the pure spectrum of S . For this purpose in section 2 we will establish some basic properties of pure and purely prime ideals of S . In section 4 we introduce the notion of quotient left S -act and investigate their properties.