On expansions of prime and 2-absorbing hyperideals in multiplicative hyperrings

Authors: GÜLŞEN ULUCAK

Abstract: In this paper, we study $ \delta $-primary and 2-absorbing $ \delta $-primary hyperideals which are the extended classes of prime and 2-absorbing hyperideals, respectively. Assume that $R$ is a commutative multiplicative hyperring with nonzero identity. We call $ I \in \mathcal{I*(R)}$ a $\delta $-primary hyperideal if $a,b\in R$ and $a\circ b\subseteq I$ imply either $a\in I$ or $b\in \delta (I)$ and also, $ I $ is called 2-absorbing $\delta $-primary hyperideal if $a,b,c\in R $ and $a\circ b\circ c \subseteq I$ imply $a\circ b\subseteq I$ or $b\circ c\subseteq \delta (I)$ or $a\circ c\subseteq \delta (I)$. Moreover, we give the basic properties of these new types of hyperideals and investigate the relations among these structures. Then a number of main results and examples are given to explain the general framework of these structures.

Keywords: $\delta$-primary hyperideal, 2-absorbing hyperideal, 2-absorbing $\delta$-primary hyperideal

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