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The goal of this first chapter is the construction of polynomial algebras GL(2) and SL(2) modelling the 2 × 2-matrices with invertible determinant [resp. with determinant equal to 1]. The multiplication of matrices induces an additional structure on these algebras. This structure is one of the basic ingredients of what will be called a Hopf algebra in Chapter III. We com-plete the chapter with various concepts of ring theory to be used in the sequel. The ground field is denoted by k.
KeywordsHopf Algebra Left Ideal Commutative Algebra Algebra Structure Free Algebra
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