We provide an expression for the conductor \(c(\varDelta )\) of a semimodule \(\varDelta \) of a numerical semigroup \(\varGamma \) with two generators in terms of the syzygy module of \(\varDelta \) and the generators of the semigroup. In particular, we deduce that the difference between the conductor of the semimodule and the conductor of the semigroup is an element of \(\varGamma \), as well as a formula for \(c(\varDelta )\) in terms of the dual semimodule of \(\varDelta \).

中文翻译：

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具有两个生成器的数值半群的半模导体的公式

我们提供用于导体的表达式\（C（\ varDelta）\）一个半模的\（\ varDelta \）的数值半群的\（\ varGamma \）与两个发电机中的对点模块而言\（\ varDelta \ ）和半群的生成器。特别是，我们推断出半模导体和半群导体之间的差是\（\ varGamma \）的元素，以及\（c（\ varDelta）\）的公式，根据\（\ varDelta \）的对偶半模块。