This paper presents the research of conditions for introducing "algebra prior to letter". In this perspective we study the potential of certain categories of generalized situations. How can they promote algebraic thinking in elementary and junior high school classes before the introduction of algebraic symbolism? In this article we show the advantage of introducing a praxeological analysis to these situations by analyzing a situation of generalization in a 6th grade class in Quebec (12-year-old students). [ABSTRACT FROM AUTHOR]
The algebra of noncommutative differential forms has been defined by A. Connes in [4]. Using this algebra, M. Karoubi has defined cyclic homology and Hochschild homology groups (see [13]). These groups are related to the algebraic K-theory. The purpose of this paper is to provide the noncommutative differential forms algebra with the structure of Gerstenhaber--Voronov algebras. [ABSTRACT FROM AUTHOR]