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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.

The optimal lower bound for generators of invariant rings without finite SAGBI bases with respect to any admissible order.

Göbel, Manfred (1999)

Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]

The order of algebras with nontrivial fixed point subalgebras.

Kureš, Miroslav, Sehnal, David (2007)

Lobachevskii Journal of Mathematics

The Picard group and subintegrality in positive characteristic

Balwant Singh (1995)

Compositio Mathematica

The Picard group of a scheme over an Artin ring

Joseph Lipman (1976)

Publications Mathématiques de l'IHÉS

The Primary components of and Integral Closures of Ideals in 3-Dimensional Regular Local Rings.

Craig Huneke (1986)

Mathematische Annalen

The prime ideals intersection graph of a ring

M. J. Nikmehr, B. Soleymanzadeh (2017)

Commentationes Mathematicae Universitatis Carolinae

Let $R$ be a commutative ring with unity and $U (R)$ be the set of unit elements of $R$ . In this paper, we introduce and investigate some properties of a new kind of graph on the ring $R$ , namely, the prime ideals intersection graph of $R$ , denoted by $G_{p} (R)$ . The $G_{p} (R)$ is a graph with vertex set $R^{*} - U (R)$ and two distinct vertices $a$ and $b$ are adjacent if and only if there exists a prime ideal $𝔭$ of $R$ such that $a, b \in 𝔭$ . We obtain necessary and sufficient conditions on $R$ such that $G_{p} (R)$ is disconnected. We find the diameter and girth of $G_{p} (R)$ ....

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The nonreduced order spectrum of a commutative ring.

The non-vanishing of the deviations of a local ring.

The number of zeros of polynomials in valuation rings of complete discretely valued fields

The Ohm type properties for multiplication ideals.

The $\circ$ operation and $*$ operation of Cohen-Macaulay bipartite graphs

The optimal lower bound for generators of invariant rings without finite SAGBI bases with respect to any admissible order.

The order of algebras with nontrivial fixed point subalgebras.

The Picard group and subintegrality in positive characteristic

The Picard group of a scheme over an Artin ring

The Primary components of and Integral Closures of Ideals in 3-Dimensional Regular Local Rings.

The prime ideals intersection graph of a ring

The product of $N$ linear forms in a field of series and the Riemann hypothesis for curves

The projective spectrum as a distributive lattice

The $Q$ -ideals in polynomial rings and the $Q$ -modules over polynomial rings.

The quasi-real extension of the real numbers

The rationality of the Poincaré series associated to the p-adic points on a variety.

The real closure of a commutative regular f-ring

The reduction number of an algebra

The reflectiveness of covering morphisms in algebra and geometry.

The Relative Separable Closure of a Valued Field in its Completion.

Currently displaying 2441 – 2460 of 2843