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Displaying 141 – 160 of 252

The moduli space of commutative algebras of finite rank

Bjorn Poonen (2008)

Journal of the European Mathematical Society

The moduli space of rank- $n$ commutative algebras equipped with an ordered basis is an affine scheme $𝔅_{n}$ of finite type over $ℤ$ , with geometrically connected fibers. It is smooth if and only if $n \leq 3$ . It is reducible if $n \geq 8$ (and the converse holds, at least if we remove the fibers above $2$ and $3$ ). The relative dimension of $𝔅_{n}$ is $\frac{2}{27} n^{3} + O (n^{8 / 3})$ . The subscheme parameterizing étale algebras is isomorphic to ${GL}_{n} / S_{n}$ , which is of dimension only $n^{2}$ . For $n \geq 8$ , there exist algebras that are not limits of étale algebras. The dimension calculations...

The Newton polygon of a product of power series.

Detlev W. Hoffmann (1994)

Manuscripta mathematica

The nilpotency of torsion-free rings with given type set

A. E. Stratton, M. C. Webb (1977)

Commentationes Mathematicae Universitatis Carolinae

The nonreduced order spectrum of a commutative ring.

James McEnerney, Gilbert Stengle (1997)

Revista Matemática de la Universidad Complutense de Madrid

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

Stephen Halperin (1987)

Commentarii mathematici Helvetici

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

Andrzej Schinzel (1984)

Fundamenta Mathematicae

The Ohm type properties for multiplication ideals.

Ali, Majid M. (1996)

Beiträge zur Algebra und Geometrie

The $\circ$ 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 $G = G_{1} \circ G_{2}$ 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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