The Huneke-Wiegand conjecture and middle terms of almost split sequences

10 Nov 2019  ·  Kobayashi Toshinori ·

Let R be a Gorenstein local domain of dimension one. We show that a nonfree maximal Cohen--Macaulay R-module M possessing more than one nonfree indecomposable summand in the middle term of the almost split sequence ending in M has a nonvanishing self extension... In other words, we show that the Huneke--Wiegand conjecture is affirmative for such R-modules M. read more

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Commutative Algebra