An EQ-algebra has three basic binary operations (meet, multiplication and a fuzzy equality) and a top element. An ℓEQ-algebra is a lattice-ordered EQ-algebra satisfying the substitution property of the join operation. In this article, we study bounded residuated ℓEQ-algebras (BR-ℓEQ-algebras for short). We introduce a subvariety RL-EQ-algebras of BR-ℓEQ-algebras, and prove that the categories of RL-EQ-algebras and residuated lattices are categorical isomorphic. We also prove that RL-EQ-algebras are precisely the BR-ℓEQ-algebras that can be reconstructed from residuated lattices. We further show the existence of a closure operator on the poset of all BR-ℓEQ-algebras with the same lattice and multiplication reduct, the existence of the maximum element in the poset. Then we introduce filters in BR-ℓEQ-algebras and give a lattice isomorphism between the filter lattice and the congruence lattice. Finally, we prove that the category of residuated lattices is isomorphic to a reflective subcategory of BR-ℓEQ-algebras.

一个 EQ 代数具有三个基本的二元运算（满足、乘法和模糊等式）和一个顶元素。一个ℓ EQ-代数是一个格有序的 EQ-代数，满足连接操作的替代性质。在本文中，我们研究了有界剩余ℓ EQ-代数（简称 BR- ℓ EQ-代数）。我们引入了BR- ℓEQ-代数的子类RL-EQ-代数，证明了RL-EQ-代数和剩余格的范畴是范畴同构的。我们还证明了 RL-EQ-代数正是可以从剩余格重构的 BR- ℓ EQ-代数。我们进一步证明了在所有 BR- ℓ的偏集上存在闭包算子具有相同格和乘法约简的 EQ 代数，存在最大元素在poset 中。然后我们在 BR- ℓ EQ-代数中引入滤波器，并给出滤波器格和同余格之间的格同构。最后，我们证明了剩余格的范畴同构于 BR - ℓ EQ-代数的反射子范畴。