ABSTRACT
A few topics connected with affine and graded algebras are studied in this chapter, e.g., Gro¨bner bases, Hilbert Nullstellensatz and affine varieties, projective closure, minimal resolutions, and Betti numbers. We present the affine and graded versions of the Noether normalization lemma and some of its applications to affine algebras and Cohen-Macaulay graded algebras.
