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This paper is a review of concepts from graded commutative algebra withspecific attention given to length and multiplicity. The author's motivationfor this paper comes from the study of equivariant cohomology in algebraictopology where the graded commutative algebra of the module is intimatelyconnected to topological properties of the space (as shown by Quillen). Results(and their proofs) which are often left as exercises, or considered 'folklore'in the commutative algebra community are included in this paper, as arereferences to relevant applications in topology. As such, this paper is aimedat algebraic topologists and geometers looking for a detailed exposition oflength and multiplicity computations in graded commutative algebra.

Length and Multiplicities in Graded Commutative Algebra