# Pasting and reversing operations over some rings

This paper examines two operations, pasting and reversing, defined as a natural mappings over some rings, such as polynomials and linear dierential operators, which is a dierential ring. We obtain some properties of these operations over these rings. This result allows us to establish some properties of natural numbers appearing in recreational mathematics.

Tipo de documento: Artículo - Article

Palabras clave: Differential rings, operators, pasting, polynomials, reversing.

Source: http://www.bdigital.unal.edu.co

## Teaser

Bol.
Mat.
17(2), 143–164 (2010) 143 Pasting and reversing operations over some rings Primitivo B.
Acosta–Humánez1 Instituto de Matemáticas y sus Aplicaciones — IMA Universidad Sergio Arboleda, Bogotá, Colombia Adriana Lorena Chuquen Escuela de Matemáticas, Universidad Sergio Arboleda Bogotá, Colombia Ángela Mariette Rodrı́guez Departamento de Fı́sica, Universidad Nacional de Colombia Bogotá, Colombia Este artı́culo examina dos operaciones, pegado e inversión, definidas como aplicaciones naturales sobre algunos anillos, tal como polinomios y operadores diferenciales lineales, el cual es un anillo diferenciable.
Se obtienen algunas propiedades de estos operadores sobre estos anillos.
Este último resultado nos permite establecer algunas propiedades de los números naturales que aparecen en matemática recreativa. Palabras claves: anillos diferenciales, operadores, pegado, polinomios, inversión. This paper examines two operations, pasting and reversing, defined as a natural mappings over some rings, such as polynomials and linear differential operators, which is a differential ring.
We obtain some properties of these operations over these rings.
This result allows us to establish some properties of natural numbers appearing in recreational mathematics. Keywords: Differential rings, operators, pasting, polynomials, reversing. MSC: 08A40, 12H05, 16S32, 97A20, 97H40. 1 primi@ima.usergioarboleda.edu.co 144 Acosta–Humánez, Chuquen and Rodrı́guez, Pasting and reversing Introduction Pasting and Reversing are common processes.
The first attempt, due to the first author, intended to interpret these natural processes as mathematical operations dates back to 1992.
One year later, he gave some lectures about the case of the natural numbers in several Colombian mathematical meetings, such as Semana de Matemáticas y Fı́sica de la Universidad del Tolima.
These lectures were published ten years later; see [2].
Recently, in 2008, the...