English

$\phi$-$\delta$-Primary Hyperideals in Krasner Hyperrings

General Mathematics 2021-12-09 v2

Abstract

In this paper, we study commutative Krasner hyperring with nonzero identity. ϕ\phi-prime, ϕ\phi-primary and ϕ\phi-δ\delta-primary hyperideals are introduced. We intend to extend the concept of δ\delta-primary hyperideals to ϕ\phi-δ\delta-primary hyperideals. We give some characterizations of hyperideals to classify them. We denote the set of all hyperideals of \Re by L()L(\Re) (all proper hyperideals of \Re by L()).L^{\ast }(\Re)). Let ϕ\phi be a reduction function such that ϕ:L()L(){}\phi:L(\Re)\rightarrow L(\Re)\cup\{\emptyset\} and δ\delta be an expansion function such that δ:L()L().\delta:L(\Re)\rightarrow L(\Re). NN be a proper hyperideal of .\Re. NN is called ϕ\phi-δ\delta-primary hyperideal of \Re if abNa\circ b\in N- ϕ(N),\phi(N), then aNa\in N or bδ(N),b\in\delta(N), for some a,b.a,b\in\Re. We\ discuss the relation between ϕ\phi-δ\delta-primary hyperideal and other hyperideals.

Cite

@article{arxiv.2111.02501,
  title  = {$\phi$-$\delta$-Primary Hyperideals in Krasner Hyperrings},
  author = {Elif Kaya and Melis Bolat and Serkan Onar and Bayram Ali Ersoy and Kostaq Hila},
  journal= {arXiv preprint arXiv:2111.02501},
  year   = {2021}
}
R2 v1 2026-06-24T07:25:11.796Z