Related papers: The Ring of Algebraic Functions on Persistence Bar…
In this paper, as an analogue of the integer case, we define congruence preserving functions over the residue class rings of polynomials over finite fields. We establish a counting formula for such congruence preserving functions, determine…
We study the algebraic and geometric properties of the integral closure of different rings of functions on a real algebraic variety : the regular functions and the continuous rational functions.
In this paper, we tackle unresolved inquiries by Ferreira et al. \cite{bruno} in their recent publication, ``Functional Identity on Division Algebras". We delve into the intricate behavior of additive functions on matrix algebras over…
The barcode of a persistence module serves as a complete combinatorial invariant of its isomorphism class. Barcodes are typically extracted by performing changes of basis on a persistence module until the constituent matrices have a special…
We define notions of differentiability for maps from and to the space of persistence barcodes. Inspired by the theory of diffeological spaces, the proposed framework uses lifts to the space of ordered barcodes, from which derivatives can be…
We obtain results describing the behavior of the action of rotation generators on polynomials over a commutative ring. We also explore harmonic polynomials in a purely algebraic setting.
The foundational character of certain algebraic structures as Boolean algebras and Heyting algebras is rooted in their potential to model classical and constructive logic, respectively. In this paper we discuss the contributions of…
The present paper studies structure of the ring of integer-valued entire functions. We characterize certain classes of prime and maximal ideals and investigate some of their properties.
In this paper, we study residues of differential 2-forms on a smooth algebraic surface over an arbitrary field and give several statements about sums of residues. Afterwards, using these results we construct algebraic-geometric codes which…
The aim of this paper is to give an algebraic characterization of the rings $C(X,\mathbb{Q}_p)$ of all continuous $\mathbb{Q}_p$-valued functions on a compact space $X$. The characterization is similar to that of M. Stone from 1940 for the…
In this paper, as an extension of the integer case, we define polynomial functions over the residue class rings of Dedekind domains, and then we give canonical representations and counting formulas for such polynomial functions. In…
Let A be the integral closure of the ring of polynomials CC[t], within the field of algebraic functions in one variable. We show that A interprets the ring of integers. This contrasts with the analogue for finite fields, proved to have a…
Looking at some monoids and (semi)rings (natural numbers, integers and p-adic integers), and more generally, residually finite algebras (in a strong sense), we prove the equivalence of two ways for a function on such an algebra to behave…
We observe algebraic derivations on an affine domain B defined over an algebraically closed field of characteristic 0, which are called locally finite derivations in commutative and non-commutative contexts in other references. We observe…
In this paper we give an effective characterization of Hilbert functions and polynomials of standard algebras over an Artinian equicharacteristic local ring; the cohomological properties of such algebras are also studied. We describe…
We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…
Persistent homology barcodes and diagrams are a cornerstone of topological data analysis that capture the "shape" of a wide range of complex data structures, such as point clouds, networks, and functions. However, their use in statistical…
The theory of persistence modules is an emerging field of algebraic topology which originated in topological data analysis. In these notes we provide a concise introduction into this field and give an account on some of its interactions…
The purpose of the present article is the study of duals of functional codes on algebraic surfaces. We give a direct geometrical description of them, using differentials. Even if this geometrical description is less trivial, it can be…
We will pursue a way of building up an algebraic structure that involves, in a mathematical abstract way, the well known Grassmann variables. The problem arises when we tried to understand the grassmannian polynomial expansion on the scope…