Turkish Journal of Mathematics
DOI
10.3906/mat-1902-41
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
First Page
1504
Last Page
1517
Recommended Citation
ULUCAK, GÜLŞEN
(2019)
"On expansions of prime and 2-absorbing hyperideals in multiplicative hyperrings,"
Turkish Journal of Mathematics: Vol. 43:
No.
3, Article 32.
https://doi.org/10.3906/mat-1902-41
Available at:
https://journals.tubitak.gov.tr/math/vol43/iss3/32
