INVERSE POLYNOMIAL MODULES INDUCED BY AN R-LINEAR MAP
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초록
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.
Abstract
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.
참고문헌 (8)
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