Álgebras e coálgebras

Abstract

The present work aims to define and exemplify algebras and coalgebras, using the tensor product. Two important results are presented, the first one, the fact that if there is a finite dimensional algebra, then when one dualizes this algebra, one constructs a coalgebra. Furthermore, the second result states that, regardless of the coalgebra considered, if it is dualized, then it is an algebra. However, before presenting such results it is necessary to review some concepts of linear algebra, and define tensor product, which is fundamental to the construction of coalgebras.