When Are Graded Rings Graded <i<S</i<-Noetherian Rings

Let <inline-formula<<math display="inline"<<semantics<<mi mathvariant="sans-serif"<Γ</mi<</semantics<</math<</inline-formula< be a commutative monoid, <inline-formula<<math display="inline"<<semantics<<...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Dong Kyu Kim [verfasserIn] Jung Wook Lim [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2020

Schlagwörter:	graded Cohen type theorem

Übergeordnetes Werk:	In: Mathematics - MDPI AG, 2013, 8(2020), 9, p 1532
Übergeordnetes Werk:	volume:8 ; year:2020 ; number:9, p 1532

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/math8091532

Katalog-ID:	DOAJ035717270

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topic_facet	<i<S</i<-Noetherian ring graded <i<S</i<-Noetherian ring <i<S</i<-finite algebra Cohen type theorem Mathematics
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callnumber-first	Q - Science
author	Dong Kyu Kim
spellingShingle	Dong Kyu Kim misc QA1-939 misc <i<S</i<-Noetherian ring misc graded <i<S</i<-Noetherian ring misc <i<S</i<-finite algebra misc Cohen type theorem misc Mathematics When Are Graded Rings Graded <i<S</i<-Noetherian Rings
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topic_title	QA1-939 When Are Graded Rings Graded <i<S</i<-Noetherian Rings <i<S</i<-Noetherian ring graded <i<S</i<-Noetherian ring <i<S</i<-finite algebra Cohen type theorem
topic	misc QA1-939 misc <i<S</i<-Noetherian ring misc graded <i<S</i<-Noetherian ring misc <i<S</i<-finite algebra misc Cohen type theorem misc Mathematics
topic_unstemmed	misc QA1-939 misc <i<S</i<-Noetherian ring misc graded <i<S</i<-Noetherian ring misc <i<S</i<-finite algebra misc Cohen type theorem misc Mathematics
topic_browse	misc QA1-939 misc <i<S</i<-Noetherian ring misc graded <i<S</i<-Noetherian ring misc <i<S</i<-finite algebra misc Cohen type theorem misc Mathematics
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title	When Are Graded Rings Graded <i<S</i<-Noetherian Rings
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title_full	When Are Graded Rings Graded <i<S</i<-Noetherian Rings
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title_sort	when are graded rings graded <i<s</i<-noetherian rings
callnumber	QA1-939
title_auth	When Are Graded Rings Graded <i<S</i<-Noetherian Rings
abstract	Let <inline-formula<<math display="inline"<<semantics<<mi mathvariant="sans-serif"<Γ</mi<</semantics<</math<</inline-formula< be a commutative monoid, <inline-formula<<math display="inline"<<semantics<<mrow<<mi<R</mi<<mo<=</mo<<msub<<mo<⨁</mo<<mrow<<mi<α</mi<<mo<∈</mo<<mi mathvariant="sans-serif"<Γ</mi<</mrow<</msub<<msub<<mi<R</mi<<mi<α</mi<</msub<</mrow<</semantics<</math<</inline-formula< a <inline-formula<<math display="inline"<<semantics<<mi mathvariant="sans-serif"<Γ</mi<</semantics<</math<</inline-formula<-graded ring and <i<S</i< a multiplicative subset of <inline-formula<<math display="inline"<<semantics<<msub<<mi<R</mi<<mn<0</mn<</msub<</semantics<</math<</inline-formula<. We define <i<R</i< to be a graded <i<S</i<-Noetherian ring if every homogeneous ideal of <i<R</i< is <i<S</i<-finite. In this paper, we characterize when the ring <i<R</i< is a graded <i<S</i<-Noetherian ring. As a special case, we also determine when the semigroup ring is a graded <i<S</i<-Noetherian ring. Finally, we give an example of a graded <i<S</i<-Noetherian ring which is not an <i<S</i<-Noetherian ring.
abstractGer	Let <inline-formula<<math display="inline"<<semantics<<mi mathvariant="sans-serif"<Γ</mi<</semantics<</math<</inline-formula< be a commutative monoid, <inline-formula<<math display="inline"<<semantics<<mrow<<mi<R</mi<<mo<=</mo<<msub<<mo<⨁</mo<<mrow<<mi<α</mi<<mo<∈</mo<<mi mathvariant="sans-serif"<Γ</mi<</mrow<</msub<<msub<<mi<R</mi<<mi<α</mi<</msub<</mrow<</semantics<</math<</inline-formula< a <inline-formula<<math display="inline"<<semantics<<mi mathvariant="sans-serif"<Γ</mi<</semantics<</math<</inline-formula<-graded ring and <i<S</i< a multiplicative subset of <inline-formula<<math display="inline"<<semantics<<msub<<mi<R</mi<<mn<0</mn<</msub<</semantics<</math<</inline-formula<. We define <i<R</i< to be a graded <i<S</i<-Noetherian ring if every homogeneous ideal of <i<R</i< is <i<S</i<-finite. In this paper, we characterize when the ring <i<R</i< is a graded <i<S</i<-Noetherian ring. As a special case, we also determine when the semigroup ring is a graded <i<S</i<-Noetherian ring. Finally, we give an example of a graded <i<S</i<-Noetherian ring which is not an <i<S</i<-Noetherian ring.
abstract_unstemmed	Let <inline-formula<<math display="inline"<<semantics<<mi mathvariant="sans-serif"<Γ</mi<</semantics<</math<</inline-formula< be a commutative monoid, <inline-formula<<math display="inline"<<semantics<<mrow<<mi<R</mi<<mo<=</mo<<msub<<mo<⨁</mo<<mrow<<mi<α</mi<<mo<∈</mo<<mi mathvariant="sans-serif"<Γ</mi<</mrow<</msub<<msub<<mi<R</mi<<mi<α</mi<</msub<</mrow<</semantics<</math<</inline-formula< a <inline-formula<<math display="inline"<<semantics<<mi mathvariant="sans-serif"<Γ</mi<</semantics<</math<</inline-formula<-graded ring and <i<S</i< a multiplicative subset of <inline-formula<<math display="inline"<<semantics<<msub<<mi<R</mi<<mn<0</mn<</msub<</semantics<</math<</inline-formula<. We define <i<R</i< to be a graded <i<S</i<-Noetherian ring if every homogeneous ideal of <i<R</i< is <i<S</i<-finite. In this paper, we characterize when the ring <i<R</i< is a graded <i<S</i<-Noetherian ring. As a special case, we also determine when the semigroup ring is a graded <i<S</i<-Noetherian ring. Finally, we give an example of a graded <i<S</i<-Noetherian ring which is not an <i<S</i<-Noetherian ring.
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container_issue	9, p 1532
title_short	When Are Graded Rings Graded <i<S</i<-Noetherian Rings
url	https://doi.org/10.3390/math8091532 https://doaj.org/article/3cfeca5647544842a6f73aa195f11161 https://www.mdpi.com/2227-7390/8/9/1532 https://doaj.org/toc/2227-7390
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We define <i<R</i< to be a graded <i<S</i<-Noetherian ring if every homogeneous ideal of <i<R</i< is <i<S</i<-finite. In this paper, we characterize when the ring <i<R</i< is a graded <i<S</i<-Noetherian ring. As a special case, we also determine when the semigroup ring is a graded <i<S</i<-Noetherian ring. 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When Are Graded Rings Graded <i<S</i<-Noetherian Rings

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