Lectures on Commutative Algebra |
Contents
INTRODUCTION | 1 |
CHAPTER TWO Prime Ideals and Radicals | 18 |
CHAPTER THREE Algebraic Manifolds | 40 |
Copyright | |
Common terms and phrases
a₁ accessible aleph algebraic extension algebraic manifold apply basis index basis theorem coefficients comaximal set common zeros complete transcendental set contradicts decomposition define denote descending chain condition distinguished polynomial domain of integrity equation equivalent F₁ F₁(x factors fib-ring with unit finite basis finite number follows formal power series Hence Hilbert homogeneous implies incomparable increasing sequence induction integers intersection irreducible set irreducibly comaximal Lemma limit aleph limit ordinal linear transformation loose chain index maximal ideal multiplicative obtain ordinal number P₁ potency preparation theorem Primary Ideals principal ideal Proof proper ideal quotient field R₁ reducible reordering result ring with unit satisfies sequence of ideals set of elements short representation t₁ total degree transcendental extension unique vanish Weierstrass Preparation Theorem whence x₁