Commutative Noetherian rings possessing a homological property

Commutative Noetherian rings possessing a homological property

For a commutative Noetherian local ring A, we have the following proposition: A is aGorenstein ring if and only if for all finitely generated A-modules M, id_AM~-is finite if andonly if pd_AM is finite. Now, we consider the following property: given a Noetherian localring A, for an arbitrary finitel...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:中国科学通报：英文版 1995 (11), p.886-889
1. Verfasser: 王明生
Format: Artikel
Sprache:eng
Schlagworte:
dimension
injective
projective
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 889
container_issue 11
container_start_page 886
container_title 中国科学通报：英文版
container_volume
creator 王明生
description For a commutative Noetherian local ring A, we have the following proposition: A is aGorenstein ring if and only if for all finitely generated A-modules M, id_AM~-is finite if andonly if pd_AM is finite. Now, we consider the following property: given a Noetherian localring A, for an arbitrary finitely generated A-module M, id_AM is finite, implying that pd_AMis finite. We ask: what ring is characterized by the above property? In this note, we firstconsider the above question; then for commutative Noetherian ring A (not necessarily lo-
format Article
fullrecord <record><control><sourceid>chongqing</sourceid><recordid>TN_cdi_chongqing_primary_3001223882</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><cqvip_id>3001223882</cqvip_id><sourcerecordid>3001223882</sourcerecordid><originalsourceid>FETCH-chongqing_primary_30012238823</originalsourceid><addsrcrecordid>eNqNjbEKwjAURTMoWLT_EHAuxKTSZnEpipOTewklJpEkL-ZFoX9vBz_A6Z7hHO6KVJzJYyN5JzakRnwyxg6t5C3rKnIaIIR3UcV9NL2BLlZnpyLNLhqkCRA14sJUUQsBPBg3KU9ThqRzmXdk_VAedf3bLdlfzvfh2kwWonkt4ZiyCyrPo1heORd9z8V_1hcqvzjq</addsrcrecordid><sourcetype>Publisher</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Commutative Noetherian rings possessing a homological property</title><source>Alma/SFX Local Collection</source><creator>王明生</creator><creatorcontrib>王明生</creatorcontrib><description>For a commutative Noetherian local ring A, we have the following proposition: A is aGorenstein ring if and only if for all finitely generated A-modules M, id_AM~-is finite if andonly if pd_AM is finite. Now, we consider the following property: given a Noetherian localring A, for an arbitrary finitely generated A-module M, id_AM is finite, implying that pd_AMis finite. We ask: what ring is characterized by the above property? In this note, we firstconsider the above question; then for commutative Noetherian ring A (not necessarily lo-</description><identifier>ISSN: 2095-9273</identifier><language>eng</language><subject>dimension ; injective ; projective</subject><ispartof>中国科学通报：英文版, 1995 (11), p.886-889</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Uhttp://image.cqvip.com/vip1000/qk/86894X/86894X.jpg</thumbnail><link.rule.ids>314,776,780,4010</link.rule.ids></links><search><creatorcontrib>王明生</creatorcontrib><title>Commutative Noetherian rings possessing a homological property</title><title>中国科学通报：英文版</title><addtitle>Chinese Science Bulletin</addtitle><description>For a commutative Noetherian local ring A, we have the following proposition: A is aGorenstein ring if and only if for all finitely generated A-modules M, id_AM~-is finite if andonly if pd_AM is finite. Now, we consider the following property: given a Noetherian localring A, for an arbitrary finitely generated A-module M, id_AM is finite, implying that pd_AMis finite. We ask: what ring is characterized by the above property? In this note, we firstconsider the above question; then for commutative Noetherian ring A (not necessarily lo-</description><subject>dimension</subject><subject>injective</subject><subject>projective</subject><issn>2095-9273</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1995</creationdate><recordtype>article</recordtype><recordid>eNqNjbEKwjAURTMoWLT_EHAuxKTSZnEpipOTewklJpEkL-ZFoX9vBz_A6Z7hHO6KVJzJYyN5JzakRnwyxg6t5C3rKnIaIIR3UcV9NL2BLlZnpyLNLhqkCRA14sJUUQsBPBg3KU9ThqRzmXdk_VAedf3bLdlfzvfh2kwWonkt4ZiyCyrPo1heORd9z8V_1hcqvzjq</recordid><startdate>1995</startdate><enddate>1995</enddate><creator>王明生</creator><scope>2RA</scope><scope>92L</scope><scope>CQIGP</scope><scope>~WA</scope></search><sort><creationdate>1995</creationdate><title>Commutative Noetherian rings possessing a homological property</title><author>王明生</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-chongqing_primary_30012238823</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1995</creationdate><topic>dimension</topic><topic>injective</topic><topic>projective</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>王明生</creatorcontrib><collection>维普_期刊</collection><collection>中文科技期刊数据库-CALIS站点</collection><collection>维普中文期刊数据库</collection><collection>中文科技期刊数据库- 镜像站点</collection><jtitle>中国科学通报：英文版</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>王明生</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Commutative Noetherian rings possessing a homological property</atitle><jtitle>中国科学通报：英文版</jtitle><addtitle>Chinese Science Bulletin</addtitle><date>1995</date><risdate>1995</risdate><issue>11</issue><spage>886</spage><epage>889</epage><pages>886-889</pages><issn>2095-9273</issn><abstract>For a commutative Noetherian local ring A, we have the following proposition: A is aGorenstein ring if and only if for all finitely generated A-modules M, id_AM~-is finite if andonly if pd_AM is finite. Now, we consider the following property: given a Noetherian localring A, for an arbitrary finitely generated A-module M, id_AM is finite, implying that pd_AMis finite. We ask: what ring is characterized by the above property? In this note, we firstconsider the above question; then for commutative Noetherian ring A (not necessarily lo-</abstract></addata></record>
fulltext fulltext
identifier ISSN: 2095-9273
ispartof 中国科学通报：英文版, 1995 (11), p.886-889
issn 2095-9273
language eng
recordid cdi_chongqing_primary_3001223882
source Alma/SFX Local Collection
subjects dimension
injective
projective
title Commutative Noetherian rings possessing a homological property
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-11T15%3A55%3A42IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-chongqing&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Commutative%20Noetherian%20rings%20possessing%20a%20homological%20property&rft.jtitle=%E4%B8%AD%E5%9B%BD%E7%A7%91%E5%AD%A6%E9%80%9A%E6%8A%A5%EF%BC%9A%E8%8B%B1%E6%96%87%E7%89%88&rft.au=%E7%8E%8B%E6%98%8E%E7%94%9F&rft.date=1995&rft.issue=11&rft.spage=886&rft.epage=889&rft.pages=886-889&rft.issn=2095-9273&rft_id=info:doi/&rft_dat=%3Cchongqing%3E3001223882%3C/chongqing%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rft_cqvip_id=3001223882&rfr_iscdi=true