arXiv subjects

Tiago Reis

Publications and source records attributed to Tiago Reis.

4 recordsLinked to original sources

arXiv2023

Characterization of the absorption radical of an evolution algebra using their associated graph

In this paper we present a method for finding the absorbing radical of a finite-dimensional evolution algebra. Such a method consists of finding the acyclic vertices of an oriented graph associated with the algebra. The set of generators associated with such vertices turn out to be the generators of the absorption radical. As an application we use the absorption radical to study the decomposability of some degenerate evolution algebras.

math.RA↗

arXiv2022

Derivations and loops of some evolution algebras

In this work we study the space of derivations of non-degenerate evolution algebras. We improve some results obtained recently in the literature and, as a consequence, we advance in the description of the derivations for $n$-dimensional Volterra evolution algebras. In addition, we introduce the notion of loop of an evolution algebra and we analyze under which conditions the set of loops is invariant under change of basis.

math.RA↗

arXiv2020

Derivations of Evolution Algebras associated to graphs over a field of any characteristic

The space of derivations of finite dimensional evolution algebras associated to graphs over a field with characteristic zero has been completely characterized in the literature. In this work we generalize that characterization by describing the derivations of this class of algebras for fields of any characteristic.

math.RA↗

arXiv2017

Gaps of powers of consecutive primes and some consequences

Let $p_n$ denote the $n$-th prime number, $\{q_n\}$ be a sequence of positive numbers and $x\in\mathbb{R}$. In this note we prove that the inequality $$q_n p_{n+1}^{x}-q_{n+1}p_{n}^{x}<p_{n}^{x}p_{n+1}^{x-1}, $$ holds for infinitely many values of $n$. As it is shown, the key ingredient to obtain this behaviour is a consequence of an extension of the Kummer's characterization of convergent series of positive terms.

math.NT↗