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Tag Archives: quaternions
The Group Algebra (III)
As alluded to at the end of the previous article, we shall consider the case where K is algebraically closed, i.e. every polynomial with coefficients in K factors as a product of linear polynomials. E.g. K = C is a common choice. Having assumed … Continue reading
Posted in Notes
Tagged character theory, division rings, group algebras, quaternions, semisimple rings, simple modules
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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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