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An algebraic extension K over a field F is a purely inseparable extension if the algebraic number minimal polynomial of any element has only one root, possibly with ...

In set theory, a unary operation on set A is a function A->A. More generally, a unary operation is a function with exactly one operand, such as the factorial, square root, or ...

If F is an algebraic Galois extension field of K such that the Galois group of the extension is Abelian, then F is said to be an Abelian extension of K. For example, ...

Starting with a triangle, draw a circle touching two sides. Then draw a circle tangent to this circle and two other sides. Continue in the same direction. The result is a ...

A branch cut is a curve (with ends possibly open, closed, or half-open) in the complex plane across which an analytic multivalued function is discontinuous. For convenience, ...

The number of "prime" boxes is always finite, where a set of boxes is prime if it cannot be built up from one or more given configurations of boxes.

Let R be a ring. If phi:R->S is a ring homomorphism, then Ker(phi) is an ideal of R, phi(R) is a subring of S, and R/Ker(phi)=phi(R).

Given n mutually exclusive events A_1, ..., A_n whose probabilities sum to unity, then P(B)=P(B|A_1)P(A_1)+...+P(B|A_n)P(A_n), where B is an arbitrary event, and P(B|A_i) is ...

A box can be packed with a harmonic brick a×ab×abc iff the box has dimensions ap×abq×abcr for some natural numbers p, q, r (i.e., the box is a multiple of the brick).

Let A, B, and C be three circles in the plane, and let X be any circle touching B and C. Then build up a chain of circles such that Y:CAX, Z:ABY, X^':BCZ, Y^':CAX^', ...