?-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:
- i) ?, ? are idempotent.
- ii) ?+?=1W.
iii) E1 and E2 .