ON SECONDARY SUBHYPERMODULES

Let r be a krasner hyperring and m be an r- hypermodule. let ψ : s h (m) → s h (m) ∪ {∅} be a function, where s h (m) denote the set of all subhypermodules of m. in the first part of this paper, we introduce the concept of a secondary hypermodule over a krasner hyperring. a non-zero hypermodule m over a krasner hyperring r is called secondary if for every r ∈ r, rm = m or r nm = 0 for some positive integer n. then we investigate some basic properties of secondary hypermodules. second, we introduce the notion of ψ-secondary subhypermodules of an r-hypermodule and we obtain some properties of such subhypermodules.