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A ring that is commutative under multiplication, has a multiplicative identity element, and has no divisors of 0. The integers form an integral domain.

An element a of a ring which is nonzero, not a unit, and whose only divisors are the trivial ones (i.e., the units and the products ua, where u is a unit). Equivalently, an ...

A noncommutative ring R is a ring in which the law of multiplicative commutativity is not satisfied, i.e., a·b!=b·a for any two elements a,b in R. In such a case, the ...

The prime subfield of a field F is the subfield of F generated by the multiplicative identity 1_F of F. It is isomorphic to either Q (if the field characteristic is 0), or ...

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 ...

The singleton set {0}, with respect to the trivial group structure defined by the addition 0+0=0. The element 0 is the additive identity element of the group, and also the ...

Algebra

Schubert's application of the conservation of number principle.

A multiplicative factor (usually indexed) such as one of the constants a_i in the polynomial a_nx^n+a_(n-1)x^(n-1)+...+a_2x^2+a_1x+a_0. In this polynomial, the monomials are ...

An exponent is the power p in an expression of the form a^p. The process of performing the operation of raising a base to a given power is known as exponentiation.