Saha, JoydipJoydipSahaSengupta, IndranathIndranathSenguptaSrivastava, PranjalPranjalSrivastava2025-08-282025-08-282024-05-01http://arxiv.org/abs/2405.11319http://repository.iitgn.ac.in/handle/IITG2025/20166This paper investigates the projective closure of simplicial affine semigroups in Nd, d?2. We present a characterization of the Cohen-Macaulay property for the projective closure of these semigroups using Gr�bner bases. Additionally, we establish a criterion, based on Gr�bner bases, for determining the Buchsbaum property of non-Cohen-Macaulay projective closures of numerical semigroup rings. Lastly, we introduce the concept of k-lifting for simplicial affine semigroups in Nd, and investigate its relationship with the original simplicial affine semigroup.en-USe-Printe-Print123456789/555