Search Results for ""

An irreducible algebraic integer which has the property that, if it divides the product of two algebraic integers, then it divides at least one of the factors. 1 and -1 are ...

If f(x) is a nonconstant integer polynomial and c is an integer such that f(c) is divisible by the prime p, that p is called a prime divisor of the polynomial f(x) (Nagell ...

When the group order h of a finite group is a prime number, there is only one possible group of group order h. Furthermore, the group is cyclic.

An Abelian planar difference set of order n exists only for n a prime power. Gordon (1994) has verified it to be true for n<2000000.

A ring for which the product of any pair of ideals is zero only if one of the two ideals is zero. All simple rings are prime.

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 ...

1 and -1 are the only integers which divide every integer. They are therefore called the prime units.

The set of prime numbers, sometimes denoted P (Derbyshire 2004, p. 163), and implemented in the Wolfram Language as Primes. In the Wolfram Language, a quantity can be tested ...

Given algebraic numbers a_1, ..., a_n it is always possible to find a single algebraic number b such that each of a_1, ..., a_n can be expressed as a polynomial in b with ...

A primitive group action is transitive and it has no nontrivial group blocks. A transitive group action that is not primitive is called imprimitive. A group that has a ...