Tag Archives: maximal ideals

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 13

Posted on March 31, 2020 by limsup

Zariski Topology for Rings In this article, we generalize earlier results in algebraic geometry to apply to general rings. Recall that points on an affine variety V correspond to maximal ideals . For general rings, we have to switch to … Continue reading →

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Commutative Algebra 11

Posted on March 29, 2020 by limsup

Coordinate Rings as k-algebras Let k be an algebraically closed field. Recall that a closed subset is identified by its coordinate ring k[V], which is a finitely generated k-algebra since Definition. An affine k-variety is a finitely generated k-algebra A which is … Continue reading →

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Introduction to Ring Theory (5)

Posted on October 25, 2012 by limsup

Our first order of the day is to state the correspondence between the ideals and subrings of R/I and those of R. This is totally analogous to the case of groups. Theorem. Let I be an ideal of R. There are 1-1 … Continue reading →

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