On 2-absorbing Primal Hyperideals Of Multiplicative Hyperrings

Mohammed M. AL-Ashker; Arwa Ashour; Sana Subouh

Mohammed M. AL-Ashker Department of Mathematics, The Islamic University of Gaza, Palestine
Arwa Ashour Department of Mathematics, The Islamic University of Gaza, Palestine
Sana Subouh Department of Mathematics, The Islamic University of Gaza, Palestine

Keywords: Multiplicative hyperring, Prime hyperideal, Primary hyperideal, irreducible hyperideal, 2-absorbing hyperideals, 2-absorbing prime hyperideals, 2-absorbing primal hyperideals.

Abstract

Let R be a commutative multiplicative hyperring. In this paper, we introduce the concept of 2-absorbing primal hyperideals. A non zero hyperideal I of a multiplicative hyperring R is called a 2-absorbing primal hyperideal of R if the set of all elements in R; that are not 2-absorbing prime to I forms a hyperideal of R; denoted (I) = fd 2 R; d is not a 2 - absorbing prime to Ig: We study properties of 2-absorbing primal hyperideals and introduce a number of results concerning 2-absorbing primal hyperideals illustrated by several examples of 2-absorbing primal hyperideals.

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