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On some properties of hyperideals in ternary hypersemirings

Manasi Mandal

Department of Mathematics, Jadavpur University, Kolkata 700032, India

E-mail Address: manasi_ju@yahoo.in

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Nita Tamang

Department of Mathematics, University of North Bengal, Siliguri 734013, India

E-mail Address: nita_anee@yahoo.in

Corresponding author.

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, and

Sampad Das

Department of Mathematics, Jadavpur University, Kolkata 700032, India

E-mail Address: jumathsampad@gmail.com

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https://doi.org/10.1142/S1793557122502308Cited by:1 (Source: Crossref)

Abstract

In this paper, we introduce the notion of prime hyperideals and maximal hyperideals in ternary hypersemirings and we study some of their properties. We construct a ternary semiring $P_{\circ} (S)$ $P_{\circ} (S)$ , corresponding to a strongly distributive ternary hypersemiring $S$ $S$ and obtain various results among them. We also establish an inclusion preserving bijection between the set of all prime hyperideals of $S$ $S$ and collection of all prime total k-ideals of $P_{\circ} (S)$ $P_{\circ} (S)$ .

Communicated by N. Gilbert

Keywords:

AMSC: 16Y60, 20N20, 16Y99

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