ABSTRACT
This chapter is preparatory in nature and we give some results on modules. We define a free module and prove that every (left) R-module is homomorphic image of a free R-module. When A,B are left R-modules and C is a right R-module, the Abelian groups https://www.w3.org/1998/Math/MathML"> H o m R ( A , B ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429204654/c7c56c01-394f-49ff-9c7d-50f6ae6e81a8/content/eq5.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> and https://www.w3.org/1998/Math/MathML"> C ⊗ R B https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429204654/c7c56c01-394f-49ff-9c7d-50f6ae6e81a8/content/eq6.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> are defined and some properties of these are obtained. The concepts of direct limit, inverse limit, pull back and push out are introduced and some properties of these are obtained.
