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A module homomorphism is a map f:M->N between modules over a ring R which preserves both the addition and the multiplication by scalars. In symbols this means that ...

If lim_(z->z_0)(f(z)-f(z_0))/(z-z_0) is the same for all paths in the complex plane, then f(z) is said to be monogenic at z_0. Monogenic therefore essentially means having a ...

sum_(k=0)^(infty)[((m)_k)/(k!)]^3 = 1+(m/1)^3+[(m(m+1))/(1·2)]^3+... (1) = (Gamma(1-3/2m))/([Gamma(1-1/2m)]^3)cos(1/2mpi), (2) where (m)_k is a Pochhammer symbol and Gamma(z) ...

A nonempty finite set of n×n integer matrices for which there exists some product of the matrices in the set which is equal to the zero matrix.

A Müntz space is a technically defined space M(Lambda)=span{x^(lambda_0),x^(lambda_1),...} which arises in the study of function approximations.

Let Omega be a space with measure mu>=0, and let Phi(P,Q) be a real function on the product space Omega×Omega. When (mu,nu) = intintPhi(P,Q)dmu(Q)dnu(P) (1) = ...

Two real algebraic manifolds are equivalent iff they are analytically homeomorphic (Nash 1952).

A negative semidefinite matrix is a Hermitian matrix all of whose eigenvalues are nonpositive. A matrix m may be tested to determine if it is negative semidefinite in the ...

Any cubic curve that passes through eight of the nine intersections of two given cubic curves automatically passes through the ninth.

A module M is Noetherian if it obeys the ascending chain condition with respect to inclusion, i.e., if every set of increasing sequences of submodules eventually becomes ...