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A subvariety of an algebraic variety that is not the entire variety. The proper subvarieties of a line are its nonempty finite subsets, the proper subvarieties of a plane are ...

The study of the nature and properties of bifurcations.

A number which can be specified implicitly or explicitly by exponential, logarithmic, and algebraic operations.

A member of the smallest algebraically closed subfield L of C which is closed under the exponentiation and logarithm operations.

Gelfond's theorem, also called the Gelfond-Schneider theorem, states that a^b is transcendental if 1. a is algebraic !=0,1 and 2. b is algebraic and irrational. This provides ...

A homogeneous ideal I in a graded ring R= direct sum A_i is an ideal generated by a set of homogeneous elements, i.e., each one is contained in only one of the A_i. For ...

The Somos sequences are a set of related symmetrical recurrence relations which, surprisingly, always give integers. The Somos sequence of order k, or Somos-k sequence, is ...

Define the zeta function of a variety over a number field by taking the product over all prime ideals of the zeta functions of this variety reduced modulo the primes. Hasse ...

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 ...

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 ...