الفهرس 
Ordered Sets, Semilattices and LatticesOnly 14 pages are availabe for public view
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Abstract
The notion of a partial module over a partial ring, equivalently, a strong semilattice of modules over a strong semilattices of rings has been used in the present work to extend basic results and constructions in the classical homological algebra-module theory. It is shown that Hom-sets of partial homomorphisms are abelian groups. The connection between exact and split exact sequences of partial modules and the corresponding exact Hom-sequences are introduced. the generalized notions of projective and injective partial modules are defined. It is shown that every free partial module is a strong semilattice of projective modules. Other results concerning direct sums and direct products of projective and injective partial modules are established. More results about the tensor products of partial modules are also given in analogy with the corresponding results in classical module theory.