ABSTRACT
One of the things which distinguishes the modern approach to Commutative Algebra is the greater emphasis on modules, rather than just on ideals. The extra “elbow-room” that this gives makes for greater clarity and simplicity. For instance, an ideal a https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429493621/dc273cdd-1d90-454a-a54f-66eaaaa4fe16/content/eq407.tif"/> and its quotient ring A / a https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429493621/dc273cdd-1d90-454a-a54f-66eaaaa4fe16/content/eq408.tif"/> are both examples of modules and so, to a certain extent, can be treated on an equal footing. In this chapter we give the definition and elementary properties of modules. We also give a brief treatment of tensor products, including a discussion of how they behave for exact sequences.
