Every Algebraic Chain Is the Congruence Lattice of a Ring Original Research Article

The equivalence of the following conditions on a chain L is proved: (1) L is algebraic; (2)There is a tight chain domain T (with identity) such that L is isomorphic to the chain of proper two-sided ideals of T and all two-sided ideals of T are idempotent; (3) L is isomorphic to the congruence lattice of a ring (not necessarily with identity).