Example image of eyePlorer eyePlorer map for 'Principal ideal domain': Abstract algebra Ideal (ring theory) Integral domain Principal ideal Zero divisor Euclidean algorithm Fundamental theorem of arithmetic Greatest common divisor Integer Dedekind domain Integrality Noetherian ring Unique factorization domain Euclidean domain Commutative ring Polynomial Eisenstein integer Gaussian integer Maximal ideal Prime ideal Integrally closed Ascending chain condition on principal ideals Bézout domain Dedekind–Hasse norm Field norm GCD domain Discrete valuation ring Elementary divisors Invariant factor Principal ideal ring Smith normal form Disk algebra Division algorithm Krull dimension List of number fields with class number one Theodore Motzkin Free ideal ring Irreducible ideal Structure theorem for finitely generated modules over a principal ideal domain Indecomposable module Nagata ring Finitely generated abelian group Hereditary ring Minimal prime (commutative algebra) Norm of an ideal Rank of an abelian group Module (mathematics) Bézout's identity Fractional ideal Functional calculus