When is C+(X) the continuous semiring?

Authors

1 Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran.

2 Faculty of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.

Abstract

In this paper, after proving some results in commutative semirings, we focus on the semiring:

C(X) of all continuous nonnegative real­valued functions on a space X with the positive operations,

and then we charactrize the space X, such that C(X) is a continuous semiring. And give some properties of the semiring.

Keywords

Main Subjects


[1] A. Peña, L. M. Ruza and J. Vielma, Separation axioms and the prime spectrum of commutative
semirings, Revista Notas de Matemática 5(2) (2009) 82-66.[2] F. Azarpanah, and O. A. S. Karamzadeh, Algebraic characterizations of some disconnected spaces,Ital. J. Pure Appl. Math. 12 (2002) 168-155.[3] L. Gillman and M. Jerison, Rings of Continuous Functions, The University Series in Higher Math.,Van Nostrand, Princeton, N. J., 1960.[4] J. S. Golan, Semirings and Their Applications, Kluwer Academic Publishers, Dordrecht, 1999.[5] J. A. Huckaba, COMMUTATIVE RINGS WITH ZERO DIVISORS, MONOGRAPHS AND TEXTBOOKSIN PURE AND APPLIED MATHEMATICS, 117. Marcel Dekker, Inc., New York, 1988.[6] P. Nasehpour, Pseudocomplementation and minimal prime ideals in semirings, Algebra Univers. 79(2018) 5-1.
[7] S. B. Niefield and K.I. Rosenthal, A note on the algebraic De Morgan’s law, Cahiers Topologie Geom.Differentielle Categ. 26 (1985) 120-115.[8] H. Subramanian, Von Neumann regularity in semirings, Math. Nachr. 45 (1970) 79-73.[9] E. M. Vechtomov, A. V. Mikhalev and V. V. Sidorov, Semirings of continuous functions, J. Math.Sci. (N.Y.) 237 (2019) 244-191.