Positive Semirings


Mathematics Department of Shahid Chamran University


In this article we investigate the positive semirings ( a semiring R is called positive if 1+x is unit for all x ε R). In fact, using the intersection of maximal ideals containing an element of a positive semiring, we give the concept of “z-ideal” in such semirings and investigate some properties of these ideals. Furthermore we study th e relations between topological properties of X and algebraic properties of positive semiring τ , where τ is the topology on X. Finally the familiar positive semiring C+(X) will be studied . Finally the familiar positive semiring C+(X) will be studied


[1] Golan, J.S. (1999). Semirings and their applications, Kluwer Academic Publisher, Dordrecht. [2] Slowikowski, W. and Zawadowski, W. (1955). A generalizayion of maximal ideals method of Stone and Gelfand, Fundamenta Mathematicae, 42(2),
215-231. [3] Willard, S. (1970). Genernl Topology, Addison Wesly, Reading Mass. [4] Gillman, L. and Jerison, M. (1960). Rings of continuous functions, Van. Nostrand Reinhold, New York. [5] Atiyah, M.F. and MacDonald, I.G. (1969). Introduction to
commutative algebra, Addison-Wesley, Reading Mass. [6] Azarpanah, F. and Mohamadian, R. (2007). √-ideals and √° - ideals in
C(X), Acta Mathematica Sinica.(Engl. Ser.), 23, 989- 996. [7] Mason, G. (1973). z-ideals and prime ideals, Journal of Algebra, 26, 280- 297. [8] Aliabad, A.R. and Mohamadian, R. (2011). sz°-ideals in polynomial rings, Communication in Algebra, Taylor & Francis Group, LLC, 39(2), 701-717. [9] Allen, P.J., Neggers, J. and Kim, H.S. (2006). Ideal theory in commutative A-semirings,
Kyungpook Mathematical. Journal, 46, 261- 271. [10] Ebrahimi Atani, S., Ebrahimi Sarvandi, Z. and Shajari Kohan, M. (2013). On primary ideals of commutative semirings, Romanian Journal of mathematics and computer science, 3, 71-81.