A CLASS OF PRIMARY SUBSEMIMODULES

The partial functions under disjoint-domain sums and functional composition is a so-ring, an algebraic structure possessing a natural partial ordering, an infinitary partial addition and a binary multiplication, subject to a set of axioms. In this paper we introduce the notion of primary subsemimodule with respect to a prime subsemimodule in partial semimodules and singular partial semiring with respect to a partial semimodule.