On k-hyperideals of semihyperrings

Abstract

In this paper we introduce the notion of k-hyperideals in semihyperrings in the sense of Krasner [11]. Also we discuss on some basic results such as the behavior of k-hyperideals under semihyperring homomorphisms and the structure of the lattice of k-hyperideals. Moreover, we characterize the k-hyperideals of a quotient semihyperrings. Also by the help of the regular equivalence relation, we construct new semihyperring and then describe all k-hyperideals of this new semihyperring.

Keywords and phrases:

• (Semi)Hyperring
• k-hyperideal
• regular equivalence relation
• homomorphism
• quotient
• lattice