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- W2372579987 abstract "0. Introduction. Let (R, m) be a regular k-spot with an infinite residue field. In [3] we had shown that every projective Rf-module is free, whenf is a regular parameter of R *. In this paper, we consider projective RfI ... ft-modules, wherefl, ... t, 1 t c d = dimension R, are regular parameters of R which are linearly independent modulo m2. When R is a formal (or convergent) power series ring over a field, it is easy to show that projective RfI.. .f-modules of rank 2 t 1 are free. If R is a regular k-spot, as above, we show that projective Rf I .. ft-modules of rank 2 t are free. In particular, every projective Rfg-module is free. When t = 1, our analysis differs from that in [3]. If, say, R /(f, ) has a coefficient field then we show that the rank t 1 projective Rf, ... ft-module is free. In general, we can capture the rank t 1 projective when d ' 2t 1. The interesting aspect of this paper is that our arguments enable us to" @default.
- W2372579987 created "2016-06-24" @default.
- W2372579987 creator A5057289307 @default.
- W2372579987 date "2016-01-01" @default.
- W2372579987 modified "2023-09-23" @default.
- W2372579987 title "ON PROJECTIVE Rf1.. ft -MODULES" @default.
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