Tag Archives: fields

Commutative Algebra 41

Posted on April 29, 2020 by limsup

Basic Definitions The objective of this article is to establish the theory of transcendence bases for field extensions. Readers who are already familiar with this may skip the article. We will focus on field extensions here. Definition. Let be a … 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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Quick Guide to Character Theory (I): Foundation

Posted on May 28, 2013 by limsup

Character theory is one of the most beautiful topics in undergraduate mathematics; the objective is to study the structure of a finite group G by letting it act on vector spaces. Earlier, we had already seen some interesting results (e.g. proof … Continue reading →

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Introduction to Ring Theory (1)

Posted on October 16, 2012 by limsup

Recall that in groups, one has only a binary operation *. Rings are algebraic structures with addition and multiplication operations – and consistency is ensured by the distributive property. Definition. A ring R is a set together with two binary operations: … Continue reading →

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