Category Archives: Advanced Algebra

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 →

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Commutative Algebra 3

Posted on March 21, 2020 by limsup

Algebraic Geometry Concepts We have decided to introduce, at this early point, some basics of algebraic geometry in order to motivate the later concepts. In summary, algebraic geometry studies solutions to polynomial equations over a field. First we consider a … Continue reading →

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Commutative Algebra 2

Posted on March 20, 2020 by limsup

Radical of an Ideal In this installation, we will study more on ideals of a ring A. Definition. If is an ideal, its radical is defined by To fix ideas, again consider the case again. For the ideal (m) where , … Continue reading →

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Commutative Algebra 1

Posted on March 19, 2020 by limsup

More About Ideals Recall that we defined three operations on ideals: intersection, sum and product. We can take intersection and sum of any collection of ideals (even infinitely many of them), but we can only define the product of finitely many … Continue reading →

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Commutative Algebra 0

Posted on March 18, 2020 by limsup

We’re starting a new series on commutative algebra. This has been in the works for way too long, and eventually we just decided to push ahead with it anyway. Most of the articles will be short, and we’ll try to … Continue reading →

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