Algebraic varieties have this property if they cannot be written as the union of other nonempty algebraic varieties. Individual elements of an integral domain have this property if they are not units, and this property holds 
Algebraic varieties have this property if they cannot be written as the union of other nonempty algebraic varieties. Individual elements of an integral domain have this property if they are not units, and this property holds when a prime number doesn't divide the first coefficient of a polynomial but does divide the rest, a condition known as Eisenstein's criterion. The pth cyclotomic polynomial always has this property for any prime number p, and if this property is not true over the rational numbers, it will not be true over the integers. For polynomials of degree two or three, this property will hold if and only if the polynomial has a zero. FTP, identify this property of polynomials, which states that any time the polynomial can be factored, one of the factors is a unit.
Algebraic varieties have this property if they cannot be written as the union of other nonempty algebraic varieties.
irreducibility (accept word forms)