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A normal extension is the splitting field for a collection of polynomials. In the case of a finite algebraic extension, only one polynomial is necessary.

A module M over a unit ring R is called flat iff the tensor product functor - tensor _RM (or, equivalently, the tensor product functor M tensor _R-) is an exact functor. For ...

In Minkowski space, a twistor may be defined as a pair consisting of a spinor field and a complex conjugate spinor field satisfying the twistor equation.

A p-adic number is an extension of the field of rationals such that congruences modulo powers of a fixed prime p are related to proximity in the so called "p-adic metric." ...

For some authors (e.g., Bourbaki, 1964), the same as principal ideal domain. Most authors, however, do not require the ring to be an integral domain, and define a principal ...

The only linear associative algebra in which the coordinates are real numbers and products vanish only if one factor is zero are the field of real numbers, the field of ...

A mathematical structure first introduced by Kolyvagin (1990) and defined as follows. Let T be a finite-dimensional p-adic representation of the Galois group of a number ...

The strongly embedded theorem identifies all simple groups with a strongly 2-embedded subgroup. In particular, it asserts that no simple group has a strongly 2-embedded ...

The set of "critical values" of a map u:R^n->R^n of map class C^1 has Lebesgue measure 0 in R^n.

If one root of the equation f(x)=0, which is irreducible over a field K, is also a root of the equation F(x)=0 in K, then all the roots of the irreducible equation f(x)=0 are ...