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Acta Mathematica Vietnamica

, Volume 44, Issue 3, pp 671–689 | Cite as

Eakin-Sathaye-Type Theorems for Joint Reductions and Good Filtrations of Ideals

  • Kriti Goel
  • Sudeshna Roy
  • J. K. VermaEmail author
Article
  • 24 Downloads

Abstract

Analogues of Eakin-Sathaye theorem for reductions of ideals are proved for \(\mathbb N^{s}\)-graded good filtrations. These analogues yield bounds on joint reduction vectors for a family of ideals and reduction numbers for \(\mathbb N\)-graded filtrations. Several examples related to lex-segment ideals, contracted ideals in 2-dimensional regular local rings and the filtration of integral and tight closures of powers of ideals in hypersurface rings are constructed to show effectiveness of these bounds.

Keywords

Eakin-Sathaye theorem Good filtrations Equimultiple good filtrations Joint reduction 

Mathematics Subject Classification (2010)

13A30 

Notes

Acknowledgments

We thank the referee for a very careful reading of the manuscript and suggesting several improvements.

Funding Information

Both of the first author and the second author are supported by UGC fellowship, Govt. of India.

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology BombayMumbaiIndia

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