We investigate the representation and complete representation classes for algebras of partial functions with the signature of relative complement and domain restriction. We provide and prove the correctness of a finite equational axiomatisation for the class of algebras representable by partial functions. As a corollary, the same equations axiomatise the algebras representable as injective partial functions. For complete representations, we show that a representation is meet complete if and only if it is join complete. Then we show that the class of completely representable algebras is precisely the class of atomic and representable algebras. As a corollary, the same properties axiomatise the class of algebras completely representable by injective partial functions. The universal-existential-universal axiomatisation this yields for these complete representation classes is the simplest possible, in the sense that no existential-universal-existential axiomatisation exists.

翻译：我们用相对补充和域限制的签名调查部分函数代数的代数和完整代数类别。我们提供并证明可以用部分函数代表的代数类别的有限等式异化的正确性。作为必然结果,同样的方程式使代数的代数具有射线部分功能的反常性。关于完整表示,我们显示完全可代表的代数类别如果并且只有在合并为完整时才完整。然后我们显示完全可代表的代数类别恰恰是原子和可代表代数的类。作为必然结果,同样的特性使代数类别完全以指向部分功能代表。普遍存在的代数生成这些完整的代数类别是最简单的,因为不存在存在-普遍代数的代数。