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A theorem proved by É. Cartan in 1913 which classifies the irreducible representations of complex semisimple Lie algebras.

When f:A->B is a ring homomorphism and b is an ideal in B, then f^(-1)(b) is an ideal in A, called the contraction of b and sometimes denoted b^c. The contraction of a prime ...

Logic is the formal mathematical study of the methods, structure, and validity of mathematical deduction and proof. According to Wolfram (2002, p. 860), logic is the most ...

Every bounded operator T acting on a Hilbert space H has a decomposition T=U|T|, where |T|=(T^*T)^(1/2) and U is a partial isometry. This decomposition is called polar ...

A reduced root system is a root system R satisfying the additional property that, if alpha in R, then the only multiples of alpha in R are +/-alpha.

A functor which defines an equivalence of module categories.

A uniquely complemented lattice is a complemented lattice (L, ^ , v ,0,1,^') that satisfies ( forall x in L)( forall y in L)[(x ^ y=0) ^ (x v y=1)]=>y=x^'. The class of ...

In geometry, the term "enlargement" is a synonym for expansion. In nonstandard analysis, let X be a set of urelements, and let V(X) be the superstructure with individuals in ...

A projection matrix P is an n×n square matrix that gives a vector space projection from R^n to a subspace W. The columns of P are the projections of the standard basis ...

Let X be a set of urelements, and let V(X) be the superstructure with X as its set of individuals. Let kappa be a cardinal number. An enlargement V(^*X) is kappa-saturated ...