Geodesic
Ideals in Ordered Γ-Semirings
Discussiones Mathematicae. General Algebra and Applications, Tome 38 (2018) no. 1, pp. 47-68.

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In this paper, we introduce the notion of k-ideal, m−k ideal, prime ideal, maximal ideal, filter, irreducible ideal, strongly irreducible ideal in ordered Γ-semirings, study the properties of ideals in ordered Γ-semirings and the relations between them. We characterize m − k ideals using derivation of ordered Γ-semirings and prove that every ideal in a mono regular ordered Γ-semiring is a prime ideal and field ordered Γ-semiring is simple.
Keywords: ordered Γ-semiring, integral ordered Γ-semiring, mono ordered Γ-semiring, prime ideal, maximal ideal, filter, irreducible ideal, strongly irreducible ideal, regular ordered Γ-semiring, k-ideal, m − k ideal 
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Rao, Marapureddy Murali Krishna. Ideals in Ordered Γ-Semirings. Discussiones Mathematicae. General Algebra and Applications, Tome 38 (2018) no. 1, pp. 47-68. http://geodesic.mathdoc.fr/item/DMGAA_2018_38_1_a3/

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