Southeast Asian Bulletin of Mathematics c  SEAMS. 2007 Southeast Asian Bulletin of Mathematics (2007) 31: 537–545 On Structure Space of Ternary Semirings S. Kar * Department of Pure Mathematics, University of Calcutta 35, Ballygunge Circular Road, Kolkata-700019, India. E-mail: karsukhendu@yahoo.co.in AMS Mathematics Subject Classification (2000): 16Y30, 16Y60 Abstract. In this paper, we introduce the notion of the structure space of ternary semirings formed by the class of prime k-ideals. We also study separation axioms and compactness property of this structure space. Finally, we investigate these properties for the structure space of the ternary semiring of non-positive integers Z - 0 . Keywords: Ternary semiring; Prime k-ideal; k-Noetherian ternary semiring; Hull-Kernel topology; Structure space. 1. Introduction In [10], L. Gillman studied ‘Rings with Hausdorff structure space’ and in [11], C. W. Kohls studied ‘The space of prime ideals of a ring’. In [1], M. R. Adhikari and M. K. Das studied ‘Structure spaces of semirings’. In [2], we introduced the notion of ternary semiring. Some works on ternary semiring may be found in [3], [4], [5], [6], [7], [8] and [9]. In this paper, we introduce and study the structure space of ternary semi- rings. We first consider the collection A of all prime k-ideals of a ternary semiring S and then we give a topology τ A on A by means of the closure operator de- fined in terms of the intersection and inclusion relation among these ideals of the ternary semiring S. We call the topological space (A,τ A ) - the structure space of the ternary semiring S. We establish the separation axioms and compactness property of this structure space. Finally, we investigate these properties for the structure space of the ternary semiring of non-positive integers Z - 0 . * The author is thankful to CSIR, India for financial assistance.