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The Brown-McCoy radical RGO for semigroups with zero is characterized in terms of modular two-sided congruences. The general notion of the e-radical of a semigroup is used to prove that RGO is the p,-class containing zero, where p. is the intersection of all modular maximal two-sided congruences of S. Thus when ps is the identity relation, RGO= 0 and S is isomorphic to a subdirect product of congruence-free semigroups with zero and identity. We also link RGO to representation theory.

Modular congruences and the Brown-McCoy radical for semigroups