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The term "higher dimensional group theory" was introduced by Brown (1982), and refers to a method for obtaining new homotopical information by generalizing to higher ...

Given a number field K, there exists a unique maximal unramified Abelian extension L of K which contains all other unramified Abelian extensions of K. This finite field ...

Let ad=bc, then Hirschhorn's 3-7-5 identity, inspired by the Ramanujan 6-10-8 identity, is given by (1) Another version of this identity can be given using linear forms. Let ...

The Hodge conjecture asserts that, for particularly nice types of spaces called projective algebraic varieties, the pieces called Hodge cycles are actually rational linear ...

A rule for polynomial computation which both reduces the number of necessary multiplications and results in less numerical instability due to potential subtraction of one ...

Horowitz reduction is used in indefinite integration to reduce a rational function into polynomial and logarithmic parts. The polynomial part is then trivially integrated, ...

The extension of a, an ideal in commutative ring A, in a ring B, is the ideal generated by its image f(a) under a ring homomorphism f. Explicitly, it is any finite sum of the ...

The radical of an ideal a in a ring R is the ideal which is the intersection of all prime ideals containing a. Note that any ideal is contained in a maximal ideal, which is ...

If a subgroup H of G has a group representation phi:H×W->W, then there is a unique induced representation of G on a vector space V. The original space W is contained in V, ...

At the age of 17, Bernard Mares proposed the definite integral (Borwein and Bailey 2003, p. 26; Bailey et al. 2006) C_2 = int_0^inftycos(2x)product_(n=1)^(infty)cos(x/n)dx ...