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If pi on V and pi^' on V^' are irreducible representations and E:V|->V^' is a linear map such that pi^'(g)E=Epi(g) for all g in and group G, then E=0 or E is invertible. ...

The problem of finding all independent irreducible algebraic relations among any finite set of quantics.

The ultraradical symbol is a notation thet can be used to express solutions not obtainable by finite root extraction. The solution to the irreducible quintic equation x^5+x=a ...

The minimal polynomial of an algebraic number zeta is the unique irreducible monic polynomial of smallest degree p(x) with rational coefficients such that p(zeta)=0 and whose ...

The following are equivalent definitions for a Galois extension field (also simply known as a Galois extension) K of F. 1. K is the splitting field for a collection of ...

A prime ideal is an ideal I such that if ab in I, then either a in I or b in I. For example, in the integers, the ideal a=<p> (i.e., the multiples of p) is prime whenever p ...

A theorem of fundamental importance in spectroscopy and angular momentum theory which provides both (1) an explicit form for the dependence of all matrix elements of ...

Gaussian brackets are notation published by Gauss in Disquisitiones Arithmeticae and defined by [ ]=1 (1) [a_1]=a_1 (2) [a_1,a_2]=[a_1]a_2+[ ] (3) ...

A field K is said to be an extension field (or field extension, or extension), denoted K/F, of a field F if F is a subfield of K. For example, the complex numbers are an ...

The finite group C_2×C_2 is one of the two distinct groups of group order 4. The name of this group derives from the fact that it is a group direct product of two C_2 ...