Abstract
In this paper, for the development of the study of almost Gorenstein graded rings, we discuss some relations between almost Gorensteinness of Cohen–Macaulay homogeneous rings and their h-vectors. Concretely, for a Cohen–Macaulay homogeneous ring R, we give a sufficient condition for R to be almost Gorenstein in terms of the h-vector of R (Theorem 3.1) and we also characterize almost Gorenstein homogeneous domains with small socle degrees in terms of the h-vector of R (Theorem 4.4). Moreover, we also provide the examples of almost Gorenstein homogeneous domains arising from lattice polytopes.
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