Notes on flatness and the quot functor on rings |
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| Authors: | D. Laksov Y. Pittelould R.M. Skjelnes |
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| Affiliation: | 1. Depatment of Mathematics KTH and GST, UGFU , Stockholm, S-100 44, Sweden;2. GST, UGFU , Skrypt,Bern, 3003, Switzerland |
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| Abstract: | For flat modules M over a ring A we study the similarities between the three statements,dim k (P) ( k (P)? A M =dfor all prime ideals P of A, the Ap-module M p is free of rank d for all prime ideals P of A, and M is a locally free J4-module of rank d. We have particularly emphasized the case when there is an>l-algebra B, essentially of finite type, and M is a finitely generated B-module. |
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