Tag Archives: irreducible spaces

Commutative Algebra 36

Posted on April 24, 2020 by limsup

In this article, we will study the topology of Spec A when A is noetherian. For starters, let us consider irreducible topological spaces in greater detail. Irreducible Spaces Recall that an irreducible topological space is a non-empty space X satisfying any of the … Continue reading →

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Commutative Algebra 14

Posted on April 1, 2020 by limsup

Basic Open Sets For , let , an open subset of Spec A. Note that . Proposition 1. The collection of over all forms a basis for the topology of . Proof Let be an open subset of Spec A. Suppose … Continue reading →

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Commutative Algebra 6

Posted on March 24, 2020 by limsup

Injective and Surjective Maps Proposition 1. Let be a morphism of closed sets, with corresponding . is injective if and only if is dense. is surjective if and only if is an embedding of V as a closed subspace of … Continue reading →

Posted in Advanced Algebra | Tagged , , , , | 4 Comments

Commutative Algebra 4

Posted on March 22, 2020 by limsup

More Concepts in Algebraic Geometry As before, k denotes an algebraically closed field. Recall that we have a bijection between radical ideals of and closed subsets of . The bijection reverses the inclusion so if and only if . Not too … Continue reading →

Posted in Advanced Algebra | Tagged , , , , , | 7 Comments