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of 29
pro vyhledávání: '"13H10, 05E40"'
Autor:
Miyashita, Sora
The nearly Gorenstein property is a generalization of the Gorenstein property. In this paper, we introduce a new property $(\natural)$ that extends the nearly Gorenstein property in semi-standard graded rings. We show $(\natural)$ relates to a proper
Externí odkaz:
http://arxiv.org/abs/2407.05629
Let $S=K[x_1,\ldots,x_n]$ and let $I$ be the $t$-path ideal of the line graph $L_n$ with $n$-vertices. It is shown that the set of associated prime ideals of $I^s$ is equal to the set of minimal prime ideals of $I$ for all $s\geq 1$, and we provide a
Externí odkaz:
http://arxiv.org/abs/2402.13477
Let $G$ be a simple graph on $n$ vertices and let $J_{G,m}$ be the generalized binomial edge ideal associated to $G$ in the polynomial ring $K[x_{ij}, 1\le i \le m, 1\le j \le n]$. We classify the Cohen-Macaulay generalized binomial edge ideals. More
Externí odkaz:
http://arxiv.org/abs/2112.15136
Autor:
Mastroeni, Matthew, McCullough, Jason
Chow rings of matroids were instrumental in the resolution of the Heron-Rota-Welsh Conjecture by Adiprasito, Huh, and Katz and in the resolution of the Top-Heavy Conjecture by Braden, Huh, Matherne, Proudfoot, and Wang. The Chow ring of a matroid is
Externí odkaz:
http://arxiv.org/abs/2111.00393
Autor:
Hibi, Takayuki, Stamate, Dumitru I.
The non-Gorenstein locus of stable set rings of finite simple perfect graphs is studied. We describe combinatorially those perfect graphs whose stable set rings are Gorenstein on the punctured spectrum. In addition, we show that, in general, for Cohe
Externí odkaz:
http://arxiv.org/abs/2108.09912
We characterize when the monomial maximal ideal of a simplicial affine semigroup ring has a monomial minimal reduction. When this is the case, we study the Cohen-Macaulay and Gorenstein properties of the associated graded ring and provide several bou
Externí odkaz:
http://arxiv.org/abs/2107.09970
We describe the simplicial complex $\Delta$ such that the initial ideal of $J_G$ is the Stanley-Reisner ideal of $\Delta$. By $\Delta$ we show that if $J_G$ is $(S_2)$ then $G$ is accessible. We also characterize all accessible blocks with whiskers o
Externí odkaz:
http://arxiv.org/abs/2107.04539
Autor:
Hibi, Takayuki, Stamate, Dumitru I.
Publikováno v:
Electronic Journal of Combinatorics 28 (3) (2021), P3.28. 11 pages
The classification of complete multipartite graphs whose edge rings are nearly Gorenstein as well as that of finite perfect graphs whose stable set rings are nearly Gorenstein is achieved.
Comment: v3: fixed one misprint in the proof of Lemma 2.
Comment: v3: fixed one misprint in the proof of Lemma 2.
Externí odkaz:
http://arxiv.org/abs/2103.17042
Autor:
Altafi, Nasrin
Publikováno v:
Proc. of the AMS-2022
We prove that a sequence $h$ of non-negative integers is the Hilbert function of some Artinian Gorenstein algebra with the strong Lefschetz property if and only if it is an SI-sequence. This generalizes the result by T. Harima which characterizes the
Externí odkaz:
http://arxiv.org/abs/2007.10684
Publikováno v:
Kyoto J. Math. 62, no. 3 (2022), 471-484
Let $S=K[x_1,\ldots,x_n]$ be the polynomial ring in $n$ variables over a field $K$. In this paper, we compute the socle of $\cb$-bounded strongly stable ideals and determine that the saturation number of strongly stable ideals and of equigenerated $\
Externí odkaz:
http://arxiv.org/abs/1909.10663