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Josimar da Silva Rocha

Publications and source records attributed to Josimar da Silva Rocha.

4 recordsLinked to original sources
arXiv2025

Classification of Associative Algebras Satisfying Quadratic Polynomial Identities

In quantum mechanics, associative algebras play an important role in understanding symmetries and operator algebras, providing new algebraic frameworks for describing physical systems. This work classifies associative algebras over a field K that are generated by a finite set G and satisfy a polynomial identity of the form X^{2} = aX+b, where a and b are elements of K and X varies either over all elements of the algebra or over all elements of the multiplicative semigroup S generated by G. One of the results obtained in this work shows that algebras satisfying X^{2}=0 over fields of characteristics different from 2 are nilpotent of index 3. The results were computationally validated using the GAP system.

math.RA↗
arXiv2019

Magic Polygons and Degenerated Magic Polygons: Characterization and Properties

In this work we define Magic Polygons P (n, k) and Degenerated Magic Polygons D(n, k) and we obtain their main properties, such as the magic sum and the value corresponding to the root vertex. The existence of magic polygons P (n, k) and degenerated magic polygons D(n, k) are discussed for certain values of n and k.

math.CO↗
arXiv2013

The n-ary Adding Machine and Soluble Groups

We describe under a variety of conditions abelian subgroups of the automorphism group A of the regular n-ary tree T which are normalized by the n-ary adding machine t=(e,...,e,t)s where s is the n-cycle (0,1,...,n-1). As an application, for n a prime number, and for n = 4 we prove that every soluble subgroup of A containing t is an extension of a torsion-free metabelian group by a finite group.

math.GR↗