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In this paper we show that the flat property of a left Rmodule does not imply (carry over) to the corresponding inverse polynomial module. Then we define an induced inverse polynomial module as an R[x]-module, i.e., given an R-linear map f : M → N of left R-modules,we define N+x−1M[x−1] as a left R[x]-module. Given an exact sequence of left R-modules 0 → N → E0 → E1 → 0,where E0,E1 injective, we show E1 + x−1E0[[x−1]] is not an injective left R[x]-module, while E0[[x−1]] is an injective left R[x]-module. Make a left R-module N as a left R[x]-module by xN = 0. We show inj dimR N = n implies inj dimR[x] N = n + 1by using the induced inverse polynomial modules and their properties.
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참고문헌 (8)
참고문헌 신청
A. S. McKerrow / 1974 / On the injective dimension of modules of power series / Quart. J. Math. Oxford Ser. 25 : 359 ~ 368
D. G. Northcott / 1974 / Injective envelopes and inverse polynomials / J. London Math. Soc. 8 : 290 ~ 296
S. Park / 1993 / Inverse polynomials and injective covers / Comm. Algebra 21 (12) : 4599 ~ 4613
S. Park / 1994 / The Macaulay-Northcott functor / Arch. Math. (Basel) 63 (3) : 225 ~ 230
S. Park / 2000 / Gorenstein rings and inverse polynomials / Comm. Algebra 28 (2) : 785 ~ 789
D. G. Northcott / 1974 / Injective envelopes and inverse polynomials / J. London Math. Soc. 8 : 290 ~ 296
S. Park / 1993 / Inverse polynomials and injective covers / Comm. Algebra 21 (12) : 4599 ~ 4613
S. Park / 1994 / The Macaulay-Northcott functor / Arch. Math. (Basel) 63 (3) : 225 ~ 230
S. Park / 2000 / Gorenstein rings and inverse polynomials / Comm. Algebra 28 (2) : 785 ~ 789
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