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The operation and * operation of Cohen-Macaulay bipartite graphs

Yulong Yang, Guangjun Zhu, Yijun Cui, Shiya Duan (2024)

Czechoslovak Mathematical Journal

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 G 2 or G = G 1 * G 2 is a graph obtained from Cohen-Macaulay bipartite graphs G 1 , G 2 by the operation or * operation, respectively.

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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