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In this chapter, we present basic concepts of commutative algebra, which are needed in the study of numerical semigroup rings. Given that graded structures naturally emerge in semigroup rings, our emphasis will be on graded rings and modules. Noetherian rings and modules, associated prime ideals, dimension theory and Hilbert series for graded modules are presented. Throughout this book R is a commutative ring with identity and K is a field, unless specified otherwise.

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Basic Commutative Algebra

  • 章节

  • 发表日期：

    2026年

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  • Jürgen Herzog,
  • Somayeh Moradi,
  • Masoomeh Rahimbeigi

摘要

In this chapter, we present basic concepts of commutative algebra, which are needed in the study of numerical semigroup rings. Given that graded structures naturally emerge in semigroup rings, our emphasis will be on graded rings and modules. Noetherian rings and modules, associated prime ideals, dimension theory and Hilbert series for graded modules are presented. Throughout this book R is a commutative ring with identity and K is a field, unless specified otherwise.