A Class of Primary Subsemimodules

Abstract

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.

Key words and phrases. Singular partial semiring wrt a partial semimodule, associated prime subsemimodule, primary partial ideal wrt a prime partial ideal, primary subsemimodule wrt a prime subsemimodule.

2000 Mathematics Subject Classification. 16Y60