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Tag Archives: fields
Commutative Algebra 41
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
Posted in Advanced Algebra
Tagged algebraic extensions, fields, transcendence basis, transcendence degree
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Commutative Algebra 0
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
Posted in Advanced Algebra
Tagged commutative rings, fields, ideals, integral domains, rings
2 Comments
Quick Guide to Character Theory (I): Foundation
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
Posted in Notes
Tagged character theory, dual spaces, fields, group algebras, groups, modules, representation theory
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Introduction to Ring Theory (1)
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
Posted in Notes
Tagged advanced, characteristic, commutative rings, distributive property, division rings, fields, integral domains, quaternions, ring theory, rings, units, zerodivisors
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