P. Fagundes

activity

20182025

most citedImages of multilinear polynomials of degree up to four on upper triangular matrices

22 citations · 29 across the 8 of their papers we have counts for

collaborators

9 papers

math.RA2025

Commutators on Generalized Block-Triangular Algebras

Pedro Souza Fagundes, Thiago Castilho de Mello

The characterization of commutators in associative algebras is a classical problem in ring theory. In this paper, we address this problem for the natural class of generalized block…

math.RA2025

Upper triangular matrices with superinvolution: identities and images of multilinear polynomials

Elena Campedel, Pedro Fagundes, Antonio Ioppolo

In this paper we consider the algebra of upper triangular matrices UT $_{n} (F)$ , endowed with a $Z_{2}$ -grading (superalgebra) and equipped with a superinvolution. These struct…

math.RA2023

f-zpd algebras and a multilinear Nullstellensatz

Ž. Bajuk, M. Brešar, P. Fagundes +1

Let $f = f (x_{1}, \dots, x_{m})$ be a multilinear polynomial over a field $F$ . An $F$ -algebra $A$ is said to be $f$ -zpd ( $f$ -zero product determined) if every $m$ -linear functional $φ\colo…

math.RA2023★ 1 cited

Values of multilinear graded $*$ -polynomials on upper triangular matrices of small dimension

Pedro Fagundes

Let $F$ be an algebraically closed field of characteristic different from $2$ . We show that the images of multilinear $*$ -polynomials on $U T_{2}$ are homogeneous vector spaces. An an…

math.RA2023

On sums of gr-PI algebras

Pedro Fagundes, Plamen Koshlukov

Let $A = B + C$ be an associative algebra graded by a group $G$ , which is a sum of two homogeneous subalgebras $B$ and $C$ . We prove that if $B$ is an ideal of $A$ , and both $B$ and $C…

math.RA2022

Images of multilinear graded polynomials on upper triangular matrix algebras

Pedro Fagundes, Plamen Koshlukov

In this paper we study the images of multilinear graded polynomials on the graded algebra of upper triangular matrices UT_n. For positive integers q \leq n, we classify these image…

math.RA2021★ 6 cited

The Mesyan Conjecture: a restatement and a correction

Pedro Souza Fagundes, Thiago Castilho de Mello, Pedro Henrique da Silva dos Santos

The well-known Lvov-Kaplansky conjecture states that the image of a multilinear polynomial $f$ evaluated on $n \times n$ matrices is a vector space. A weaker version of this conject…

math.RA2018★ 22 cited

Images of multilinear polynomials of degree up to four on upper triangular matrices

Pedro S. Fagundes, Thiago C. de Mello

We describe the images of multilinear polynomials of degree up to four on the upper triangular matrix algebra.

math.RA2018

The images of multilinear polynomials on strictly upper triangular matrices

Pedro S. Fagundes

The purpose of this paper is to describe the images of multilinear polynomials of arbitrary degree on the strictly upper triangular matrix algebra.