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Completely ${\mathfrak m}$-full ideals and componentwise linear ideals

Published online by Cambridge University Press:  10 December 2014

TADAHITO HARIMA  and
JUNZO WATANABE
TADAHITO HARIMA
Affiliation:
Department of Mathematics Education, Niigata University, Niigata 950-2181, Japan. e-mail: [email protected]
JUNZO WATANABE
Affiliation:
Department of Mathematics, Tokai University, Hiratsuka 259-1292, Japan. e-mail: [email protected]
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Abstract

We show that the class of completely ${\mathfrak m}$-full ideals coincides with the class of componentwise linear ideals in a polynomial ring over an infinite field.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 158 , Issue 2 , March 2015 , pp. 239 - 248
Copyright
Copyright © Cambridge Philosophical Society 2014 

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References

REFERENCES

[1]Conca, A.Reduction number and initial ideals. Proc. Amer. Math. Soc. 131 (2003), 1015–1020.CrossRefGoogle Scholar
[2]Goto, S.Integral closedness of complete-intersection ideals. J. Algebra. 108 (1987), 151–160.CrossRefGoogle Scholar
[3]Goto, S. and Hayasaka, F.Finite homological dimension and primes associated to integrally closed ideals. Proc. Amer. Math. Soc. 130 (2002) 3159–3164.CrossRefGoogle Scholar
[4]Green, M. L.Generic initial ideals. Six Lectures on Commutative Algebra. Birkhäuser Verlag, Basel. Prog. Math. 166 (1998), 119–186.CrossRefGoogle Scholar
[5]Herzog, J. and Hibi, T.Componentwise linear ideals. Nagoya Math. J. 153 (1999), 141–153.CrossRefGoogle Scholar
[6]Harima, T. and Watanabe, J.The weak Lefschetz property for ${\mathfrak m}$-full ideals and componentwise linear ideals. Illinois J. Math. 156 (2012), 957–966.Google Scholar
[7]Nagel, U. and Römer, T.Criteria for componentwise linearity. Commun. Algebra. 43 (2015), 1–18.CrossRefGoogle Scholar
[8]Watanabe, J.${\mathfrak m}$-full ideals. Nagoya Math. J. 106 (1987), 101–111.CrossRefGoogle Scholar
[9]Watanabe, J.The syzygies of ${\mathfrak m}$-full ideals. Math. Proc. Camb. Phil. Soc. 109 (1991), 7–13.CrossRefGoogle Scholar
[10]Watanabe, J.${\mathfrak m}$-full ideals II. Math. Proc. Camb. Phil. Soc. 111 (1992), 231–240.CrossRefGoogle Scholar