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This chapter focuses on the canonical ideal of a numerical semigroup and symmetry properties. We begin by presenting the canonical ideal and key aspects of relative ideals. The notions of pseudo-symmetric and almost symmetric numerical semigroups are then introduced, with a particular focus on their characterization and examples involving 3 generators. Finally, we discuss nearly symmetric numerical semigroups and their connection to almost symmetric numerical semigroups, concluding with an analysis of the canonical trace for 3-generated numerical semigroups.

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Almost Symmetric and Nearly Symmetric Numerical Semigroups

  • 章节

  • 发表日期：

    2026年

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  • Jürgen Herzog,
  • Somayeh Moradi,
  • Masoomeh Rahimbeigi

摘要

This chapter focuses on the canonical ideal of a numerical semigroup and symmetry properties. We begin by presenting the canonical ideal and key aspects of relative ideals. The notions of pseudo-symmetric and almost symmetric numerical semigroups are then introduced, with a particular focus on their characterization and examples involving 3 generators. Finally, we discuss nearly symmetric numerical semigroups and their connection to almost symmetric numerical semigroups, concluding with an analysis of the canonical trace for 3-generated numerical semigroups.