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

可交换的剩余格\（{\ varvec {A}} \）被说成是subidempotent如果它的中性元素的下限ë是幂等的（在这种情况下，它们自然构成布劳威尔格代数\（{\ varvec {A}} ^-\））。在这里证明，在每个有（或没有对合）代数\ {{\ varvec {A}} \\}（有或没有对合）的情况下，同质化在各种\ {{\ mathsf {K}} \}中都是射影的，只要每个有限次直接不可约代数\（{\ varvec {B}} \\ {\ mathsf {K}} \中的）具有两个属性：（1）  \（{\ varvec {B}} \）由e的下限生成，而（2）\（{\ varvec {B}} ^-\）的质数过滤器的位姿具有有限的深度。（1）和（2）均不可丢弃。证明适应边界的存在。该结果概括了G. Bezhanishvili和前两位作者有关Brouwerian代数，Heyting代数和Sugihara id半体中的种子表位的最新发现，但其范围也涵盖了一系列有趣的De Morgan id半体。