On Superfluous Subsemimodules

Abstract

Abstract This paper considers superfluous subsemimodules and some applications of them to projective covers of semimodules. The following notions are introduced: a superfluous ∧-subsemimodule, a 𝑘-quasiregular homomorphism, a radical of a ∧-semimodule, a projective cover, and a semiring satisfying the condition 0–1. We present some characteristic properties of superfluous subsemimodules and give some applications of them to projective covers of semimodules, analogous to applications of superfluous submodules to projective covers of modules.