Epimorphisms in varieties of subidempotent residuated structures

A commutative residuated lattice is said to be subidempotent if the lower bounds of its neutral element e are idempotent (in which case they naturally constitute a Brouwerian algebra A*). It proved here that epimorphisms surjective in variety K such algebras (with or without involution), provided each finitely subdirectly irreducible B has two properties: (1) generated by e, and (2) poset prime filters B* finite depth. Neither nor may dropped. The proof adapts presence bounds. result generalizes some recent findings G. Bezhanishvili first authors concerning varieties algebras, Heyting Sugihara monoids, but scope also encompasses range interesting De Morgan monoids.