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The field axioms are generally written in additive and multiplicative pairs. name addition multiplication associativity (a+b)+c=a+(b+c) (ab)c=a(bc) commutativity a+b=b+a ...

A mathematical object invented to solve irreducible congruences of the form F(x)=0 (mod p), where p is prime.

A coordinate system which has a metric satisfying g_(ii)=-1 and partialg_(ij)/partialx_j=0.

A linear transformation A:R^n->R^n is hyperbolic if none of its eigenvalues has modulus 1. This means that R^n can be written as a direct sum of two A-invariant subspaces E^s ...

The axis in the complex plane corresponding to zero real part, R[z]=0.

Given F_1(x,y,z,u,v,w) = 0 (1) F_2(x,y,z,u,v,w) = 0 (2) F_3(x,y,z,u,v,w) = 0, (3) if the determinantof the Jacobian |JF(u,v,w)|=|(partial(F_1,F_2,F_3))/(partial(u,v,w))|!=0, ...

Every finite-dimensional Lie algebra of characteristic p!=0 has a faithful finite-dimensional representation.

The partial differential equation u_t+2uu_x-nuu_(xx)+muu_(xxx)=0.

The second-order ordinary differential equation y^('')+k/xy^'+epsilony^'y=0.

Let K be a finite complex, let h:|K|->|K| be a continuous map. If Lambda(h)!=0, then h has a fixed point.