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Let be a commutative ring with identity. A regular ideal
of
is stable if
is a projective over its ring of endomorphisms. If every regular ideal of
is stable, then
is said to be stable. In the first half of a two-part study, we describe the basic structural properties of stable integral domains.
I thank Silvana Bazzoni for a close reading of the first version of the two parts of this paper and for her many helpful comments and corrections.
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