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Tag Archives: fields
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, zero-divisors
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