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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 $\Int_{M}(R)$, the ring of integer-valued polynomials on $R$ over $M$. We establish some properties of Krull dimensions of $\Int(R,M)$ and $\Int_{M}(R)$. We also determine when $\Int(R,M)$ and $\Int_{M}(R)$ are nontrivial. Among the other results, it is shown that $\Int(\mathbb{Z},M)$ is not Noetherian module over $\Int_{M}(\mathbb{Z})\cap\Int(\mathbb{Z})$, where $M$ is a finitely generated $\mathbb{Z}$-module.
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참고문헌 (28)
참고문헌 신청
P.-J. Cahen / 1997 / Integer-valued polynomials / American Mathematical Society
J. Dauns / 1978 / Prime modules / Journal für die reine und angewandte Mathematik (Crelles Journal) 1978(298):156~181
Jesse Elliott / 2011 / Integer-valued polynomial rings, t-closure, and associated primes / Communications in Algebra 39(11):4128~4147
JESSE ELLIOTT / 2012 / PRESENTATIONS AND MODULE BASES OF INTEGER-VALUED POLYNOMIAL RINGS / Journal of Algebra and Its Applications 12(01):1250137
Jesse Elliott / 2017 / Integer-valued polynomials on commutative rings and modules / Communications in Algebra 46(3):1121~1137
J. Dauns / 1978 / Prime modules / Journal für die reine und angewandte Mathematik (Crelles Journal) 1978(298):156~181
Jesse Elliott / 2011 / Integer-valued polynomial rings, t-closure, and associated primes / Communications in Algebra 39(11):4128~4147
JESSE ELLIOTT / 2012 / PRESENTATIONS AND MODULE BASES OF INTEGER-VALUED POLYNOMIAL RINGS / Journal of Algebra and Its Applications 12(01):1250137
Jesse Elliott / 2017 / Integer-valued polynomials on commutative rings and modules / Communications in Algebra 46(3):1121~1137
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