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- W1569754263 abstract "0. Introduction. The purpose of this paper is to consider the following question: if R is a regular Noetherian ring and S ⊃ R is a module-finite R -algebra, is R a direct summand of S as R -modules? An affirmative answer is given if R contains a field, and it is shown that if the completions of the local rings of S possess maximal Cohen-Macaulay modules in the sense of § 1 of [6] then the conclusion is valid in this case too. Hence, if Conjecture E of [6] is true then the question raised here has an affirmative answer without further restriction on the regular Noetherian ring R , and it will be shown here that only a greatly weakened version of Conjecture E is needed." @default.
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- W1569754263 date "1973-09-01" @default.
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- W1569754263 title "Contracted ideals from integral extensions of regular rings" @default.
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- W1569754263 doi "https://doi.org/10.1017/s0027763000015701" @default.
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