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| INJECTIVE PRECOVERS AND MODULES OF GENERALIZED INVERSE POLYNOMIALS |
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Citation： |
LIU Zhongkui.INJECTIVE PRECOVERS AND MODULES OF GENERALIZED INVERSE POLYNOMIALS[J].Chinese Annals of Mathematics B,2004,25(1):129~138 |
| Page view： 1248
Net amount： 747 |
Authors： |
LIU Zhongkui; |
Foundation： |
Project supported by the National Natural Science Foundation of China (No.10171082), the Teaching
and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of the
Ministry of Education of China and NWNU-KJCXGC212. |
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| Abstract： |
This paper is motivated by S. Park [10] in which the injective
cover of left $R[x]$-module $M[x^{-1}]$ of inverse polynomials
over a left $R$-module $M$ was discussed. The author considers the
$\boldsymbol\Omega$-covers of modules and shows that if $\eta:
P\longrightarrow M$ is an $\boldsymbol\Omega$-cover of $M$, then
$[\eta^{S, \leq}]: [P^{S, \leq}]\longrightarrow [M^{S, \leq}]$ is
an $[\boldsymbol\Omega^{S, \leq}]$-cover of left $[[R^{S,
\leq}]]$-module $[M^{S, \leq}]$, where $\boldsymbol\Omega$ is a
class of left $R$-modules and $[M^{S, \leq}]$ is the left $[[R^{S,
\leq}]]$-module of generalized inverse polynomials over a left
$R$-module $M$. Also some properties of the injective cover of
left $[[R^{S, \leq}]]$-module $[M^{S, \leq}]$ are discussed. |
Keywords： |
Injective precover, $\boldsymbol\Omega$-cover, Module of generalized
inverse polynomials, Ring of generalized power series |
Classification： |
16W60 |
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