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The Eisenbud-Evans Generalized Principal Ideal Theorem and Determinantal Ideals

1981
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Proceedings of the American Mathematical Society
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In [2] Eisenbud and Evans gave an important generalization of Krull's Principal Ideal Theorem. However, their proof, using maximal Cohen-Macaulay modules, may have limited the validity of their theorem to a proper subclass of all local rings. (Höchster proved the existence of maximal Cohen-Macaulay modules for local rings which contain a field, cf. [4]). In the first section we present a proof which is simpler and guarantees the Generalized Principal Ideal Theorem for all local rings. The main

doi:10.2307/2043882
fatcat:62doywdlcfg5pk5hujwamepx4m