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An extension A subset B of a group, ring, module, field, etc., such that A!=B.

A power series containing fractional exponents (Davenport et al. 1993, p. 91) and logarithms, where the logarithms may be multiply nested, e.g., lnlnx.

A commutative unit ring having only finitely many maximal ideals.

A regular local ring is a local ring R with maximal ideal m so that m can be generated with exactly d elements where d is the Krull dimension of the ring R. Equivalently, R ...

A ringoid is a set R with two binary operators, conventionally denoted addition (+) and multiplication (×), where × distributes over + left and right: a(b+c)=ab+ac and ...

If Li_2(x) denotes the usual dilogarithm, then there are two variants that are normalized slightly differently, both called the Rogers L-function (Rogers 1907). Bytsko (1999) ...

A second countable space is a topological space whose topology is second countable.

A semiring is a set together with two binary operators S(+,*) satisfying the following conditions: 1. Additive associativity: For all a,b,c in S, (a+b)+c=a+(b+c), 2. Additive ...

A conjecture that, as proved by Parshin (1968), implies the Mordell conjecture.

Let A and B be two *-algebras. An algebraic homomorphism phi:A->B is called *-homomorphism if it satisfies phi(a^*)=phi(a)^* for each a in A.