The rank rk(R) of a ring R is the supremum of minimal cardinalities of generating sets of I as I ranges over ideals of R. Matsuda and Matson showed that every n is an element of Z(+) (the positive integers) occurs as the rank of some ring R. Motivated by the result of Cohen and Gilmer that a ring of finite rank has Krull dimension 0 or 1, we give four different constructions of rings of rank n (for all n is an element of Z(+)). Two constructions use one-dimensional domains. Our third construction uses Artinian rings (dimension zero), and our last construction uses polynomial rings over local Artinian rings (dimension one, irreducible, not a domain).
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