Class of Semihyperrings from Partitions of a Set

Abstract

In this paper we show that a partition {P α : α ∈ Λ} of a non-empty set S, where Λ is an ordered set with the least element α 0 and P α 0 is a singleton set, induces a hyperaddition + such that (S,+) is a commutative hypermonoid. Also by using a collection of subsets of S, induced by the partition of the set S, we define hypermultiplication on S so that (S,+,·) is a semihyperring.

Keywords

• hypermonoid, semihyperring, ∗-collection