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2‐Prime Hyperideals of Multiplicative Hyperrings

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  • Mahdi Anbarloei

Abstract

Multiplicative hyperrings are an important class of algebraic hyperstructures which generalize rings further to allow multiple output values for the multiplication operation. Let R be a commutative multiplicative hyperring. A proper hyperideal I of R is called 2‐prime if x∘y⊆I for some x, y ∈ R, then, x2⊆I or y2⊆I. The 2‐prime hyperideals are a generalization of prime hyperideals. In this paper, we aim to study 2‐prime hyperideals and give some results. Moreover, we investigate δ‐2‐primary hyperideals which are an expansion of 2‐prime hyperideals.

Suggested Citation

  • Mahdi Anbarloei, 2022. "2‐Prime Hyperideals of Multiplicative Hyperrings," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:5721946
    DOI: 10.1155/2022/5721946
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    References listed on IDEAS

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    1. Anastase Nakassis, 1988. "Recent results in hyperring and hyperfield theory," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 11, pages 1-12, January.
    2. Marc Krasner, 1983. "A class of hyperrings and hyperfields," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 6, pages 1-5, January.
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