Abstract
Let R be a commutative regular ring, and let R* be the Boolean ring of idempotents in R. It is well known that the mappings J1-4f = JCR* and i-47 = RI are reciprocal lattice isomorphisms between ideals of R and ideals of R*. In this paper we make these mappings into functors:Toeach 4 EHomR(Jl, J2), respectivelyI'eHomR*(II, I2), we associate a homomorphism 'CHomR*(Jl, f2), respectively *CeHomR(Il, 72). Using these constructions, we prove that the endomorphism ring of an ideal of R is regular, and that the homological dimension of an ideal is equal to its homological dimension as a module over its endomorphism ring. For each xEzR let x* be the (unique) idempotent such that Rx* =Rx. We will use the following relations repeatedly:
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