Stability of Depth and Cohen-Macaulayness of Integral Closures of Powers of Monomial Ideals
Let I be a monomial ideal in a polynomial ring R = k [ x 1 , … , x r ] . In this paper, we give an upper bound on dstab ¯ ( I ) in terms of r and the maximal generating degree d ( I ) of I such that depth R / I n ¯ is constant for all n ⩾ dstab ¯ ( I ) . As an application, we classify the class of m...
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| Veröffentlicht in: | Acta mathematica vietnamica 2018-03, Vol.43 (1), p.67-81 |
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| container_title | Acta mathematica vietnamica |
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| creator | Hoa, Le Tuan Trung, Tran Nam |
| description | Let
I
be a monomial ideal in a polynomial ring
R
=
k
[
x
1
,
…
,
x
r
]
. In this paper, we give an upper bound on
dstab
¯
(
I
)
in terms of
r
and the maximal generating degree
d
(
I
) of
I
such that
depth
R
/
I
n
¯
is constant for all
n
⩾
dstab
¯
(
I
)
. As an application, we classify the class of monomial ideals
I
such that
I
n
¯
is Cohen-Macaulay for some integer
n
≫ 0. |
| doi_str_mv | 10.1007/s40306-017-0225-0 |
| format | Article |
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I
be a monomial ideal in a polynomial ring
R
=
k
[
x
1
,
…
,
x
r
]
. In this paper, we give an upper bound on
dstab
¯
(
I
)
in terms of
r
and the maximal generating degree
d
(
I
) of
I
such that
depth
R
/
I
n
¯
is constant for all
n
⩾
dstab
¯
(
I
)
. As an application, we classify the class of monomial ideals
I
such that
I
n
¯
is Cohen-Macaulay for some integer
n
≫ 0.</description><identifier>ISSN: 0251-4184</identifier><identifier>EISSN: 2315-4144</identifier><identifier>DOI: 10.1007/s40306-017-0225-0</identifier><language>eng</language><publisher>Singapore: Springer Singapore</publisher><subject>Closures ; Mathematics ; Mathematics and Statistics ; Upper bounds</subject><ispartof>Acta mathematica vietnamica, 2018-03, Vol.43 (1), p.67-81</ispartof><rights>Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2017</rights><rights>Copyright Springer Science & Business Media 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-f86e91e78270fcab5e574e267d3898a3c9b7258d65016e8d4ab05e5e1c5b44e33</citedby><cites>FETCH-LOGICAL-c316t-f86e91e78270fcab5e574e267d3898a3c9b7258d65016e8d4ab05e5e1c5b44e33</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s40306-017-0225-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s40306-017-0225-0$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Hoa, Le Tuan</creatorcontrib><creatorcontrib>Trung, Tran Nam</creatorcontrib><title>Stability of Depth and Cohen-Macaulayness of Integral Closures of Powers of Monomial Ideals</title><title>Acta mathematica vietnamica</title><addtitle>Acta Math Vietnam</addtitle><description>Let
I
be a monomial ideal in a polynomial ring
R
=
k
[
x
1
,
…
,
x
r
]
. In this paper, we give an upper bound on
dstab
¯
(
I
)
in terms of
r
and the maximal generating degree
d
(
I
) of
I
such that
depth
R
/
I
n
¯
is constant for all
n
⩾
dstab
¯
(
I
)
. As an application, we classify the class of monomial ideals
I
such that
I
n
¯
is Cohen-Macaulay for some integer
n
≫ 0.</description><subject>Closures</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Upper bounds</subject><issn>0251-4184</issn><issn>2315-4144</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1UEtLw0AQXkTBUvsDvAU8R2df2c1R4qvQoqCePCybZNJG0mzdTZD-e7etBy8ehm-Y7zHwEXJJ4ZoCqJsggEOWAlUpMCZTOCETxqlMBRXilEyASRp3Lc7JLIS2BMpVBkrLCfl4HWzZdu2wS1yT3OF2WCe2r5PCrbFPl7ayY2d3PYaw5-f9gCtvu6ToXBg9Ho4v7hv9YVu63m3aSM9rtF24IGdNBJz94pS8P9y_FU_p4vlxXtwu0orTbEgbnWFOUWmmoKlsKVEqgSxTNde5trzKS8WkrjMJNENdC1tC1CCtZCkEcj4lV8fcrXdfI4bBfLrR9_GloXnOuFBxoooeVZV3IXhszNa3G-t3hoLZ12iONZpYo9nXaCB62NETorZfof-T_K_pB-TRdDA</recordid><startdate>20180301</startdate><enddate>20180301</enddate><creator>Hoa, Le Tuan</creator><creator>Trung, Tran Nam</creator><general>Springer Singapore</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20180301</creationdate><title>Stability of Depth and Cohen-Macaulayness of Integral Closures of Powers of Monomial Ideals</title><author>Hoa, Le Tuan ; Trung, Tran Nam</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-f86e91e78270fcab5e574e267d3898a3c9b7258d65016e8d4ab05e5e1c5b44e33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Closures</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Upper bounds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hoa, Le Tuan</creatorcontrib><creatorcontrib>Trung, Tran Nam</creatorcontrib><collection>CrossRef</collection><jtitle>Acta mathematica vietnamica</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hoa, Le Tuan</au><au>Trung, Tran Nam</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Stability of Depth and Cohen-Macaulayness of Integral Closures of Powers of Monomial Ideals</atitle><jtitle>Acta mathematica vietnamica</jtitle><stitle>Acta Math Vietnam</stitle><date>2018-03-01</date><risdate>2018</risdate><volume>43</volume><issue>1</issue><spage>67</spage><epage>81</epage><pages>67-81</pages><issn>0251-4184</issn><eissn>2315-4144</eissn><abstract>Let
I
be a monomial ideal in a polynomial ring
R
=
k
[
x
1
,
…
,
x
r
]
. In this paper, we give an upper bound on
dstab
¯
(
I
)
in terms of
r
and the maximal generating degree
d
(
I
) of
I
such that
depth
R
/
I
n
¯
is constant for all
n
⩾
dstab
¯
(
I
)
. As an application, we classify the class of monomial ideals
I
such that
I
n
¯
is Cohen-Macaulay for some integer
n
≫ 0.</abstract><cop>Singapore</cop><pub>Springer Singapore</pub><doi>10.1007/s40306-017-0225-0</doi><tpages>15</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0251-4184 |
| ispartof | Acta mathematica vietnamica, 2018-03, Vol.43 (1), p.67-81 |
| issn | 0251-4184 2315-4144 |
| language | eng |
| recordid | cdi_proquest_journals_1992347234 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Closures Mathematics Mathematics and Statistics Upper bounds |
| title | Stability of Depth and Cohen-Macaulayness of Integral Closures of Powers of Monomial Ideals |
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