Let d and tt be positive integers with n >= d + 1 and 03 C Rd an integral cyclic polytope of dimension d with tt vertices, and let K[P]= K[Z(>= 0)A(p)] denote its associated semigroup K-algebra, where A(p) = {(1, alpha) is an element of Rd+1 is an element of alpha is an element of P} boolean AND Z(d+1) and K is a field. In the present paper, we consider the problem when K[P] is Cohen-Macaulay by discussing Serre's condition (R-1), and we give a complete characterization when K[P] is Gorenstein. Moreover, we study the normality of the other semigroup K-algebra K[Q] arising from an integral cyclic polytope, where Q is a semigroup generated by its vertices only.
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机译：设d和tt为n> = d + 1的正整数，并且03 C Rd为具有tt个顶点的，维数为d的整数循环多边形，并令K [P] = K [Z（> = 0）A（p）]表示与其关联的半群K代数，其中A（p）= {（1，alpha）是Rd + 1的元素是alpha的元素是P的元素}布尔AND Z（d + 1）并且K是一个字段。在本文中，我们通过讨论Serre条件（R-1）来考虑K [P]为Cohen-Macaulay时的问题，并且当K [P]为Gorenstein时给出完整的刻画。此外，我们研究了由整数环状多位点引起的另一个半群K-代数K [Q]的正态性，其中Q是仅由其顶点生成的半群。
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