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

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 is an element of I* (R.) a delta-primary hyperideal if a, b is an element of R and a circle b subset of I imply either a is an element of I or b is an element of delta(I) and also, I is called 2-absorbing delta-primary hyperideal if a, b, c is an element of R and a circle b circle c subset of I imply a circle b subset of I or b circle c subset of delta(I) or a circle c subset of 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.