Numerical semigroup rings are investigated from the relative viewpoint. It is known that algebraic properties such as singularities of a numerical semigroup ring are properties of a flat numerical semigroup algebra. In this paper, we show that arithmetic and set-theoretic properties of a numerical semigroup ring are properties of an equi-gcd numerical semigroup algebra.

中文翻译：

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数值半群代数的系数环

从相对的角度研究了数值半群环。众所周知，数值半群环的奇点等代数性质是平坦数值半群代数的性质。在本文中，我们证明了数值半群环的算术和集合论性质是等 gcd 数值半群代数的性质。