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In the original formulation, a quantity associated with ideal class groups. According to Chevalley's formulation, a Grössencharakter is a multiplicative character of the ...

A test which always identifies prime numbers correctly, but may incorrectly identify a composite number as a prime.

There are two important theorems known as Herbrand's theorem. The first arises in ring theory. Let an ideal class be in A if it contains an ideal whose lth power is ...

Find two distinct sets of integers {a_1,...,a_n} and {b_1,...,b_n}, such that for k=1, ..., m, sum_(i=1)^na_i^k=sum_(i=1)^nb_i^k. (1) The Prouhet-Tarry-Escott problem is ...

Also called Macaulay ring, a Cohen Macaulay ring is a Noetherian commutative unit ring R in which any proper ideal I of height n contains a sequence x_1, ..., x_n of elements ...

An algebraic ring which appears in treatments of duality in algebraic geometry. Let A be a local Artinian ring with m subset A its maximal ideal. Then A is a Gorenstein ring ...

Model completion is a term employed when existential closure is successful. The formation of the complex numbers, and the move from affine to projective geometry, are ...

Given a nonzero finitely generated module M over a commutative Noetherian local ring R with maximal ideal M and a proper ideal I of R, the Hilbert-Samuel function of M with ...

A double Mersenne number is a number of the form M_(M_n)=2^(2^n-1)-1, where M_n is a Mersenne number. The first few double Mersenne numbers are 1, 7, 127, 32767, 2147483647, ...

B_(p+k)=B_k+B_(k+1) (mod p), when p is prime and B_n is a Bell number.