INVERSE POLYNOMIAL MODULES INDUCED BY AN R-LINEAR MAP

Title & Authors
INVERSE POLYNOMIAL MODULES INDUCED BY AN R-LINEAR MAP
Park, Sang-Won; Jeong, Jin-Sun;

Abstract
In this paper we show that the flat property of a left R-module 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 $\small{\rightarrow}$ N of left R-modules, we define $\small{N+x^{-1}M[x^{-1}]}$ as a left R[x]-module. Given an exact sequence of left R-modules $\small{0\;{\rightarrow}\;N\;{\rightarrow}\;E^0\;{\rightarrow}\;E^1\;{\rightarrow}\;0}$, where $\small{E^0}$, $\small{E^1}$ injective, we show $\small{E^1\;+\;x^{-1}E^0[[x^{-1}]]}$ is not an injective left R[x]-module, while $\small{E^0[[x^{-1}]]}$ is an injective left R[x]-module. Make a left R-module N as a left R[x]-module by xN
Keywords
flat module;injective module;inverse polynomial module;induced module;
Language
English
Cited by
1.
PROPERTIES OF INDUCED INVERSE POLYNOMIAL MODULES OVER A SUBMONOID,;;

Korean Journal of Mathematics, 2012. vol.20. 3, pp.307-314
1.
PROPERTIES OF INDUCED INVERSE POLYNOMIAL MODULES OVER A SUBMONOID, Korean Journal of Mathematics, 2012, 20, 3, 307
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