Principal Ideal Domains

Abbreviation: PIDom

Definition

A principal ideal domain is an integral domain R = (R, + ,−,0,·,1) in which
every ideal is principal:   ∀I  ∈ Idl(R) ∃a  ∈ R (I = aR)
Ideals are defined for commutative rings

Morphisms

Some results

Examples

{a + bθ| a,b ∈ Z, θ = (1 + (−19)^1/2)/2} is a Principal Ideal Domain that is not an Euclidean domain
See Oscar Campoli's "A Principal Ideal Domain That Is Not a Euclidean Domain" in The American Mathematical Monthly 95 (1988): 868-871

Properties

Finite members

Subclasses

Superclasses