Magmatic Gr(?)bner-Shirshov Basis Of A Free Gelfand-Dorfman-Novikov Algebra And Composition-Diamond Lemma For Grassmann Algebra And Its Tensor Product

In the first part of this thesis, we found a magmatic Gr?bner-Shirshov basis of a free Gelfand-Dorfman-Novikov algebra such that the corresponding set of irreducible magmatic words is the Dzhumadildaev-L?fwall linear basis of the Gelfand-Dorfman-Novikov algebra. In the second part, we consider the Composition-Diamond lemma for Grassmann algebra. Firstly, we establish the Composition-Diamond lemma for the Grassmann algebras over a field. Secondly, we give Composition-Diamond lemma for Grassmann algebra over commutative algebra. Finally, we give Composition-Diamond lemma for the tensor product of Grassmann algebras over a field.