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

Abstract

In this paper, we study -primary and 2-absorbing -primary hyperideals which are the extended classes ofprime and 2-absorbing hyperideals, respectively. Assume that R is a commutative multiplicative hyperring with nonzeroidentity. We call I 2 I (R) a -primary hyperideal if a; b 2 R and a ◦ b I imply either a 2 I or b 2 (I) andalso, I is called 2-absorbing -primary hyperideal if a; b; c 2 R and a ◦ b ◦ c I imply a ◦ b I or b ◦ c (I) ora ◦ c (I) . Moreover, we give the basic properties of these new types of hyperideals and investigate the relationsamong these structures. Then a number of main results and examples are given to explain the general framework ofthese structures.