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Associated with an irreducible curve of curve genus p, there are p linearly independent integrals of the first sort. The roots of the integrands are groups of the canonical ...

There is a one-to-one correspondence between the sets of equivalent correspondences (not of value 0) on an irreducible curve of curve genus p, and the rational collineations ...

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 ...

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 ...