模上整数多项式的一些结果

IF 0.6 4区数学 Q3 MATHEMATICS

Bulletin of the Korean Mathematical Society Pub Date : 2020-01-01 DOI:10.4134/BKMS.B190846

A. Naghipour, J. S. Hafshejani

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引用次数: 0

摘要

设M是交换环R上的一个模，本文研究了M / R上的整值多项式模Int(R,M)和R / M上的整值多项式环IntM (R)。我们建立了Int(R,M)和IntM (R)的Krull维的一些性质，并确定了Int(R,M)和IntM (R)在什么情况下是非平凡的。在其他结果中，证明了Int(Z,M)不是IntM (Z)∩Int(Z)上的Noetherian模，其中M是一个有限生成的Z模。

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SOME RESULTS ON INTEGER-VALUED POLYNOMIALS OVER MODULES

Let M be a module over a commutative ring R. In this paper, we study Int(R,M), the module of integer-valued polynomials on M over R, and IntM (R), the ring of integer-valued polynomials on R over M . We establish some properties of Krull dimensions of Int(R,M) and IntM (R). We also determine when Int(R,M) and IntM (R) are nontrivial. Among the other results, it is shown that Int(Z,M) is not Noetherian module over IntM (Z) ∩ Int(Z), where M is a finitely generated Z-module.

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来源期刊

Bulletin of the Korean Mathematical Society 数学-数学

CiteScore

0.80

自引率

20.00%

发文量

审稿时长

6 months

期刊介绍： This journal endeavors to publish significant research of broad interests in pure and applied mathematics. One volume is published each year, and each volume consists of six issues (January, March, May, July, September, November).