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

Gülşen ULUCAK

Makale detayları

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

Yazarlar:

Gülşen ULUCAK

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2019 Vol.43 Issue 3, pp.1504-1517

Belge Tipi:

Makale

Yayın Tarihi:

5/2019

Belge Dili:

Türkçe

Document ID (Org No.):

2000745612

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Özet:

 

In this paper, we study δδ \delta -primary and 2-absorbing δδ \delta -primary hyperideals which are the extended classes of prime and 2-absorbing hyperideals, respectively. Assume that RRR is a commutative multiplicative hyperring with nonzero identity. We call I∈I∗(R)I∈I∗(R) I \in \mathcal{I*(R)} a δδ\delta -primary hyperideal if a,b∈Ra,b∈Ra,b\in R and a∘b⊆Ia∘b⊆Ia\circ b\subseteq I imply either a∈Ia∈Ia\in I or b∈δ(I)b∈δ(I)b\in \delta (I) and also, II I  is called  2-absorbing δδ\delta -primary hyperideal if a,b,c∈Ra,b,c∈Ra,b,c\in R  and a∘b∘c⊆Ia∘b∘c⊆Ia\circ b\circ c \subseteq I imply a∘b⊆Ia∘b⊆Ia\circ b\subseteq I or b∘c⊆δ(I)b∘c⊆δ(I)b\circ c\subseteq \delta (I) or a∘c⊆δ(I)a∘c⊆δ(I)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.

Makale detayları

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

Yazarlar: Gülşen ULUCAK

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2019 Vol.43 Issue 3, pp.1504-1517

Belge Tipi: Makale

Yayın Tarihi: 5/2019

Belge Dili: Türkçe

Document ID (Org No.): 2000745612

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

Gülşen ULUCAK

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2019 Vol.43 Issue 3, pp.1504-1517

Belge Tipi:

Makale

Yayın Tarihi:

5/2019

Belge Dili:

Türkçe

Document ID (Org No.):

2000745612

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098