Liaqat Ali,Yaqoub Ahmed Khan,Muhammad Aslam,



Monomial Ideals,Prime Spectrum,Topological Semirings,Zariski Topology,


In this article, we introduce the monomial ideals of semirings and study some of its properties. Main objective of this articleis to investigate prime spectrum of monomial ideals of semirings and discuss its topology.


I. A. Dochtermann and A. Engstrom, Algebraic properties of edge ideals via combinatorial topology, Electron. J. Combin., vol. 16, no. 2 pp. 16-23,2009.

II. A. I. Barvinok, Combinatorial Optimization and Computations in the Ring of Polynomials, DIMACS Technical Report, pp. 93-103,1993
III. H. Ansari-Toroghy, R. Ovlyaee-Sarmazdeh, On the prime spectrum of a module and Zariski topologies, Comm. Algebra, vol. 38, pp. 4461-4475, 2010.

IV. H.S Vandiver, Note on a simple type of algebra in which the cancellation law of addition does not hold, Bull. Amer. Math. Soc. vol. 40, No. 12, pp. 914-920, 1934.

V. J. Herzog and T. Hibi, Monomial ideals, Springer, 2011.

VI. J. S. Golan, Semirings and their applications,Kluwer Acad. Pub. Dodrecht,1999.

VII. P. J. Allen, A fundamental theorem of homomorphisms for simirings, Proc. Amer. Math. Soc., pp. 412-416, 1969.

VIII. R. Arens, J. Dugundji, Remark on the concept of compactness, Portugaliae Math., vol. 9, pp. 141-143, 1950.

IX. R. E. Atani and S. E. Atani, Ideal theory in commutative semirings, Bul. Acad. Stiinue Repub. Mold. Mat., vol. 2, pp. 14–23,2008.

X. R. E. Atani and S. E. Atani, Some remarks on partitioning semirings, An. St. Univ. Ovidius Constanta, vol. 18, pp. 49-62, 2010.

XI. R. Y. McCasland, M. E. Moore and P. F. Smith, On the spectrum of a module over a commutative ring, Comm. Algebra, vol. 25, pp. 79–103, 1997.

XII. S. Ballal and V. Kharat, Zariski topology on lattice modules, Asian-Eur. J.Math., vol. 8, no. 4 pp. 10-21, 2015

XIII. S. E. Atani, The ideal theory in quotients of commutative semirings, Glasnik Mat., vol. 42, pp. 301-308, 2007.

XIV. S. Eilenberg, Automata, languages, and machines, Academic Press, New York,vol. A, 1974.

XV. S. Hosten, G.G. Smith, Monomial ideals. InComputations in algebraic geometry with Macaulay 2, Algorithms and Computations in Mathematics, vol. 8, pp.73–100, 2011.

XVI. T.K. Mukherjee, M. K. Sen and S. Ghosh, Chain conditions on semirings, Internat. J. Math. and Math. Sci., vol. 19 no. 2, pp. 321-326, 1996.

View Download