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If N is a submodule of the module M over the ring R, the quotient group M/N has a natural structure of R-module with the product defined by a(x+N)=ax+N for all a in R and all ...

A group or other algebraic object is called non-Abelian if the law of commutativity does not always hold, i.e., if the object is not Abelian. For example, the group of ...

For a Galois extension field K of a field F, the fundamental theorem of Galois theory states that the subgroups of the Galois group G=Gal(K/F) correspond with the subfields ...

The inverse erf function is the inverse function erfc^(-1)(z) of erfc(x) such that erfc(erfc^(-1)(x))=erfc^(-1)(erfc(x)), (1) with the first identity holding for 0<x<2 and ...

By way of analogy with the eban numbers, uban numbers are defined as numbers whose English names do not contain the letter "u" (i.e., "u" is banned). Note that this ...

Conjugation is the process of taking a complex conjugate of a complex number, complex matrix, etc., or of performing a conjugation move on a knot. Conjugation also has a ...

A function is said to be modular (or "elliptic modular") if it satisfies: 1. f is meromorphic in the upper half-plane H, 2. f(Atau)=f(tau) for every matrix A in the modular ...

Let E be an elliptic curve defined over the field of rationals Q(sqrt(-d)) having equation y^2=x^3+ax+b with a and b integers. Let P be a point on E with integer coordinates ...

An affine transformation is any transformation that preserves collinearity (i.e., all points lying on a line initially still lie on a line after transformation) and ratios of ...

In logic, the term "homomorphism" is used in a manner similar to but a bit different from its usage in abstract algebra. The usage in logic is a special case of a "morphism" ...