?-Injective Semimodule over Semiring

Abstract

?-injective modules over a ring have been studied by many authors. Quasi-continuous modules is another name of this concept.

   In this work ?-injective semimodule over a semiring will be introduced and investigated. If W is a semimodule over a semiring R then W is said to be ?-injective if for any two subsemimodulesE₁, E₂ of W with E₁?E₂=0, there exist?, ? ?End(W) such that:

1. i) ?, ? are idempotent.
2. ii) ?+?=1_W.

iii) E₁  and E₂ .