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International Journal of Algebra and Computation· 2026Q2

Comparison of Stability Indices of Powers of Graded Ideals

Antonino Ficarra, Emanuele Sgroi

Short summary

A 2-dimensional polynomial ring allows for any positive integer value for the index of ass-stability of graded ideal powers.

AI-generated from the title and abstract; the full text is not read.

Key points

  • For graded ideals in a 2-dimensional polynomial ring, the ass-stability index is less than or equal to the [Formula: see text]-stability index.
  • The [Formula: see text]-stability index of graded ideals in a 2-dimensional polynomial ring can be any positive integer.
  • A method is provided to construct graded ideals in [Formula: see text]-dimensional polynomial rings to achieve specific stability index relationships.

AI-generated from the title and abstract; the full text is not read.

Abstract

In this paper, we compare the index of ass-stability [Formula: see text] and the index of [Formula: see text]-stability [Formula: see text] of powers of a graded ideal [Formula: see text]. We prove that [Formula: see text] for any graded ideal [Formula: see text] in a 2-dimensional polynomial ring, and that [Formula: see text] can be any positive integer in this situation. Moreover, given any integers [Formula: see text], we construct a graded ideal [Formula: see text] in a [Formula: see text]-dimensional polynomial ring such that [Formula: see text].

The authors' abstract, as published at the source. International Journal of Algebra and Computation, 2026 · DOI ↗

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Field: Algebra and Number Theory

Algebra and Number TheoryMathematics