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Information Journal Paper

Title

Canonical module of Cohen-Macaulay affine semigroup

Pages

  93-98

Abstract

 Let S be a simplicial affine semigroup of dimension r and R=K[[S]] be the semigroup ring assigned to S, where K is a field. Then R is a Noetherian ring of krull dimension r. When r=1, S is a numerical semigroup whose assigned semigroup ring is a one dimensional Cohen-Macaulay ring. In this case, all each set of S is a finite set, and the number of its maximal elements with respect to the natural relation, is equal to the type of R. But in general, when r>1, the Apery sets of S are not necessarily finite. In this paper, we introduce r Apery sets of S whose intersection is a finite set and determines the type and the canonical module of R. This set coincides with an Apery set, when r=1. In particular, we extend the known facts about canonical module of numerical semigroups to all Cohen-Macaulay simplicial affine semigroups.

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    • Cite

    APA: Copy

    JAFARI, RAHELEH. (2022). Canonical module of Cohen-Macaulay affine semigroup. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 6(27 ), 93-98. SID. https://sid.ir/paper/951826/en

    Vancouver: Copy

    JAFARI RAHELEH. Canonical module of Cohen-Macaulay affine semigroup. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2022;6(27 ):93-98. Available from: https://sid.ir/paper/951826/en

    IEEE: Copy

    RAHELEH JAFARI, “Canonical module of Cohen-Macaulay affine semigroup,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 6, no. 27 , pp. 93–98, 2022, [Online]. Available: https://sid.ir/paper/951826/en

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