All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 2 Next

Displaying 21 – 40 of 67

Showing per page

The higher transvectants are redundant

Abdelmalek Abdesselam, Jaydeep Chipalkatti (2009)

Annales de l’institut Fourier

Let A , B denote generic binary forms, and let 𝔲 r = ( A , B ) r denote their r -th transvectant in the sense of classical invariant theory. In this paper we classify all the quadratic syzygies between the { 𝔲 r } . As a consequence, we show that each of the higher transvectants { 𝔲 r : r ≥ 2 } is redundant in the sense that it can be completely recovered from 𝔲 0 and 𝔲 1 . This result can be geometrically interpreted in terms of the incomplete Segre imbedding. The calculations rely upon the Cauchy exact sequence of S L 2 -representations, and the...

The ideal of relations for the ring of invariants of n points on the line

Benjamin Howard, John J. Millson, Andrew Snowden, Ravi Vakil (2012)

Journal of the European Mathematical Society

The ring of projective invariants of n ordered points on the projective line is one of the most basic and earliest studied examples in Geometric Invariant Theory. It is a remarkable fact and the point of this paper that, unlike its close relative the ring of invariants of n unordered points, this ring can be completely and simply described. In 1894 Kempe found generators for this ring, thereby proving the First Main Theorem for it (in the terminology introduced by Weyl). In this paper we compute...

The maximal regular ideal of some commutative rings

Emad Abu Osba, Melvin Henriksen, Osama Alkam, Frank A. Smith (2006)

Commentationes Mathematicae Universitatis Carolinae

In 1950 in volume 1 of Proc. Amer. Math. Soc., B. Brown and N. McCoy showed that every (not necessarily commutative) ring R has an ideal 𝔐 ( R ) consisting of elements a for which there is an x such that a x a = a , and maximal with respect to this property. Considering only the case when R is commutative and has an identity element, it is often not easy to determine when 𝔐 ( R ) is not just the zero ideal. We determine when this happens in a number of cases: Namely when at least one of a or 1 - a has a von Neumann inverse,...

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.

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 ∈ 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 ) ....

Currently displaying 21 – 40 of 67