Tensor product of partial modules

Abstract

In this article partial modules over rings and tensor product of partial modules and its properties are studied. Left and right partial modules, partial bimodules and their homomorphisms are defined. Next, partial quotient modules are defined and the fundamental homomorphism theorem for partial modules is proven. Also, the tensor product of partial modules and the tensor product of homomorphisms of partial modules is defined. Some properties of the tensor product, the existence of hom-functors and tensor functors are proven. Finally it is shown that the hom-functor and the tensor functor are adjoint functors.