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Let $G$ be a finite simple graph with the vertex set $V$ and let $I_{G}$ be its edge ideal in the polynomial ring $S = 𝕂 [V]$ . We compute the depth and the Castelnuovo-Mumford regularity of $S / I_{G}$ when $G = G_{1} \circ G_{2}$ or $G = G_{1} * G_{2}$ is a graph obtained from Cohen-Macaulay bipartite graphs $G_{1}$ , $G_{2}$ by the $\circ$ operation or $*$ operation, respectively.

Two applications of dualizing complexes over local rings

Paul Roberts (1976)

Annales scientifiques de l'École Normale Supérieure

Über das Verhalten der Betti-Reihe eines lokalen Ringes bei monoidalen Transformationen

J. DASSOW (1975)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

Ueber die minimale Dimension der assoziierten Primideale der Komplettion eines lokalen Integritätsbereiches.

Markus Brodmann (1975)

Commentarii mathematici Helvetici

Un exemple d'anneau caténaire

A. Bouvier, F. Burq, G. Germain (1980)

Publications du Département de mathématiques (Lyon)

Valuations and lengths of constructible modules.

P. Ribenboim (1976)

Journal für die reine und angewandte Mathematik

Vanishing Tensor Powers of Modules.

Roger Wiegand, Sylvia Wiegand (1972)

Mathematische Zeitschrift

When is each proper overring of R an S(Eidenberg)-domain?

Noômen Jarboui (2002)

Publicacions Matemàtiques

A domain R is called a maximal "non-S" subring of a field L if R ⊂ L, R is not an S-domain and each domain T such that R ⊂ T ⊆ L is an S-domain. We show that maximal "non-S" subrings R of a field L are the integrally closed pseudo-valuation domains satisfying dim(R) = 1, dimv(R) = 2 and L = qf(R).

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