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Stable trace ideals and applications.

Hailong Dao1, Haydee Lindo2

  • 1Department of Mathematics, University of Kansas, Lawrence, KS 66045-7523 USA.

Collectanea Mathematica (Barcelona, Spain)
|April 1, 2024
PubMed
Summary

This study explores stable trace ideals within one-dimensional local Cohen-Macaulay rings. These findings offer new insights and applications in commutative algebra.

Area of Science:

  • Commutative Algebra
  • Ring Theory

Background:

  • Local Cohen-Macaulay rings are fundamental in commutative algebra.
  • Trace ideals are crucial for understanding ring structures.

Purpose of the Study:

  • To investigate the properties of stable trace ideals.
  • To explore applications of these ideals in one-dimensional local Cohen-Macaulay rings.

Main Methods:

  • Utilizing techniques from homological algebra.
  • Analyzing the structure of ideals in specific ring types.

Main Results:

  • Characterization of stable trace ideals in the studied rings.
  • Demonstration of several novel applications stemming from these ideals.

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Conclusions:

  • Stable trace ideals provide a powerful tool for analyzing one-dimensional local Cohen-Macaulay rings.
  • The identified applications broaden the scope of their utility in algebraic research.