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- W2991340719 abstract "The purpose of this paper is triple. First off, for an equi-characteristic zero, or a p-torsion free (0, p)-mixed characteristic local ring, we settle, positively, the conjecture on the closedness of the category of modules of finite complete intersection dimension under taking finite direct sums. Secondly, a question proposed by Celikbas, Takahashi and Dao, is answered, again affirmatively, for all (local) rings. This second question asks whether a local ring possessing a (pd-)test module of finite complete intersection dimension has to be a complete intersection? Lastly, in the category of local rings with uncountable residue field, we show that a question raised by Celikbas and Wagstaff has positive answer. This third question asks whether (pd-)test complexes ascend under flat local homomorphisms with regular closed fiber?" @default.
- W2991340719 created "2019-12-05" @default.
- W2991340719 creator A5047760712 @default.
- W2991340719 date "2019-11-26" @default.
- W2991340719 modified "2023-09-27" @default.
- W2991340719 title "A Trilogy, Given By Complete Tensor Product of Complete Rings Over The Coefficient Ring" @default.
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