# Algebra Commons™

## All Articles in Algebra

893 full-text articles. Page 1 of 33.

2018 Georgia State University

#### 33 - On The Existence Of An Arbitrarily Large Number Of Generators For The Presentation Ideal Of A Semigroup Ring., Arun Suresh

##### Georgia Undergraduate Research Conference (GURC)

Consider K to be an arbitrary field, and P(n1,…, nm) be the ideal of polynomials given by

P(n1,…, nm) = {f(x1, … , xm) : f(x1,…,xm) ∈ K[x1,…,xm], f(tn1, … ,tnm) = 0, where t is transcendental over K}.

In 1970, J. Herzog showed that the least upper bound on the number of generators of K, for m = 3, is 3. It can be lowered to two, if n1, n2, n3 satisfy a few symmetry conditions. Following that, Bresinsky in 1975, showed ...

On Projection Of A Positive Definite Matrix On A Cone Of Nonnegative Definite Toeplitz Matrices, 2018 Poznań University Of Technology

#### On Projection Of A Positive Definite Matrix On A Cone Of Nonnegative Definite Toeplitz Matrices, Katarzyna Filipiak, Augustyn Markiewicz, Adam Mieldzioc, Aneta Sawikowska

##### Electronic Journal of Linear Algebra

We consider approximation of a given positive definite matrix by nonnegative definite banded Toeplitz matrices. We show that the projection on linear space of Toeplitz matrices does not always preserve nonnegative definiteness. Therefore we characterize a convex cone of nonnegative definite banded Toeplitz matrices which depends on the matrix dimensions, and we show that the condition of positive definiteness given by Parter [{\em Numer. Math. 4}, 293--295, 1962] characterizes the asymptotic cone. In this paper we give methodology and numerical algorithm of the projection basing on the properties of a cone of nonnegative definite Toeplitz matrices. This problem can be ...

Explicit Block-Structures For Block-Symmetric Fiedler-Like Pencils, 2018 University of California, Santa Barbara

#### Explicit Block-Structures For Block-Symmetric Fiedler-Like Pencils, M. I. Bueno, Madeline Martin, Javier Perez, Alexander Song, Irina Viviano

##### Electronic Journal of Linear Algebra

In the last decade, there has been a continued effort to produce families of strong linearizations of a matrix polynomial $P(\lambda)$, regular and singular, with good properties, such as, being companion forms, allowing the recovery of eigenvectors of a regular $P(\lambda)$ in an easy way, allowing the computation of the minimal indices of a singular $P(\lambda)$ in an easy way, etc. As a consequence of this research, families such as the family of Fiedler pencils, the family of generalized Fiedler pencils (GFP), the family of Fiedler pencils with repetition, and the family of generalized Fiedler pencils with ...

On The Largest Distance (Signless Laplacian) Eigenvalue Of Non-Transmission-Regular Graphs, 2018 East China Normal University