2000 character limit reached
Conditions of multiplicity and applications for almost Gorenstein graded rings (2311.17387v3)
Published 29 Nov 2023 in math.AC and math.CO
Abstract: In this paper, we prove that if Cohen-Macaulay local/graded rings $R_1$, $R_2$ and $R$ satisfy certain conditions regarding multiplicity and Cohen-Macaulay type, then almost Gorenstein property of $R$ implies Gorenstein properties for all of $R_1$, $R_2$ and $R$. We apply our theorem to tensor products of semi-standard graded rings and some classes of affine semigroup rings, i.e., numerical semigroup rings, edge rings and stable set rings.
- W. Bruns and J. Herzog. Cohen–Macaulay rings. Number 39. Cambridge university press, 1998.
- C. Delorme. Sous-monoïdes d’intersection complète de ℕℕ\mathbb{N}blackboard_N. Ann. Scient. École Norm. Sup.(9), 1998.
- D. R. Grayson and M. E. Stillman. Macaulay2, a software system for research in algebraic geometry. Available at http://www2.macaulay2.com.
- J. Herzog and E. Kunz. Die werthalbgruppe eines lokalen rings der dimension 1. Ber. Heidelberger Akad. Wiss, 1971.
- S. Miyashita. Comparing generalized Gorenstein properties in semi-standard graded rings. arXiv:2309.09221, 2023.
- H. Ohsugi and T. Hibi. Normal polytopes arising from finite graphs. J. Algebra, 207(2):409–426, 1998.
- R. Villarreal. Monomial algebras. CRC press, 2018.
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