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A module M over a unit ring R is called faithfully flat if the tensor product functor - tensor _RM is exact and faithful. A faithfully flat module is always flat and ...

The modular group Gamma is the set of all transformations w of the form w(t)=(at+b)/(ct+d), where a, b, c, and d are integers and ad-bc=1. A Gamma-modular function is then ...

A gigantic prime is a prime with 10000 or more decimal digits. The first few gigantic primes are given by 10^(9999)+n for n=33603, 55377, 70999, 78571, 97779, 131673, 139579, ...

The second-order ordinary differential equation (d^2y)/(dx^2)+[theta_0+2sum_(n=1)^inftytheta_ncos(2nx)]y=0, (1) where theta_n are fixed constants. A general solution can be ...

A hole in a mathematical object is a topological structure which prevents the object from being continuously shrunk to a point. When dealing with topological spaces, a ...

For an n×n matrix, let S denote any permutation e_1, e_2, ..., e_n of the set of numbers 1, 2, ..., n, and let chi^((lambda))(S) be the character of the symmetric group ...

The (lower) irredundance number ir(G) of a graph G is the minimum size of a maximal irredundant set of vertices in G. The upper irredundance number is defined as the maximum ...

A minimal dominating set is a dominating set in a graph that is not a proper subset of any other dominating set. Every minimum dominating set is a minimal dominating set, but ...

A proof which indirectly shows a mathematical object exists without providing a specific example or algorithm for producing an example. Nonconstructive proofs are also called ...

Consider the average volume of a tetrahedron picked at random inside an octahedron of unit volume. The answer is difficult to compute analytically (Zinani 2003), but the mean ...