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The polynomials in the diagonal of the Smith normal form or rational canonical form of a matrix are called its invariant factors.

The Davenport constant of a finite Abelian group G is defined to be the length of the longest minimal zero-system of G and is denoted D(G). Symbolically, ...

The essential supremum is the proper generalization to measurable functions of the maximum. The technical difference is that the values of a function on a set of measure zero ...

Let alpha_i and A_i be algebraic numbers such that the A_is differ from zero and the alpha_is differ from each other. Then the expression ...

A nonzero module M over a ring R whose only submodules are the module itself and the zero module. It is also called a simple module, and in fact this is the name more ...

A ring homomorphism is a map f:R->S between two rings such that 1. Addition is preserved:f(r_1+r_2)=f(r_1)+f(r_2), 2. The zero element is mapped to zero: f(0_R)=0_S, and 3. ...

A class of game in which players move alternately and each player is completely informed of previous moves. Finite, zero-sum, two-player games with perfect information ...

Nonhomogeneous matrix equations of the form Ax=b (1) can be solved by taking the matrix inverse to obtain x=A^(-1)b. (2) This equation will have a nontrivial solution iff the ...

An equation derived by Kronecker: where r(n) is the sum of squares function, zeta(z) is the Riemann zeta function, eta(z) is the Dirichlet eta function, Gamma(z) is the gamma ...

There does not exist an everywhere nonzero tangent vector field on the 2-sphere S^2. This implies that somewhere on the surface of the Earth, there is a point with zero ...