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Gaussian curvature, sometimes also called total curvature (Kreyszig 1991, p. 131), is an intrinsic property of a space independent of the coordinate system used to describe ...

Let P be the set of prime ideals of a commutative ring A. Then an affine scheme is a technical mathematical object defined as the ring spectrum sigma(A) of P, regarded as a ...

Let A be a commutative complex Banach algebra. A nonzero homomorphism from A onto the field of complex numbers is called a character. Every character is automatically ...

A polyhedron in a hyperbolic geometry.

Module multiplicity is a number associated with every nonzero finitely generated graded module M over a graded ring R for which the Hilbert series is defined. If dim(M)=d, ...

A relation "<=" is a partial order on a set S if it has: 1. Reflexivity: a<=a for all a in S. 2. Antisymmetry: a<=b and b<=a implies a=b. 3. Transitivity: a<=b and b<=c ...

Given a module M over a commutative unit ring R and a filtration F:... subset= I_2 subset= I_1 subset= I_0=R (1) of ideals of R, the Rees module of M with respect to F is ...

Given a commutative unit ring R and a filtration F:... subset= I_2 subset= I_1 subset= I_0=R (1) of ideals of R, the Rees ring of R with respect to F is R_+(F)=I_0 direct sum ...

B^^ = T^^xN^^ (1) = (r^'xr^(''))/(|r^'xr^('')|), (2) where the unit tangent vector T and unit "principal" normal vector N are defined by T^^ = (r^'(s))/(|r^'(s)|) (3) N^^ = ...

A bundle map is a map between bundles along with a compatible map between the base manifolds. Suppose p:X->M and q:Y->N are two bundles, then F:X->Y is a bundle map if there ...