Abstract In this paper we define the monadic pseudo BE-algebras and investigate their properties. We prove that the existential and universal quantifiers of a monadic pseudo BE-algebra form a residuated pair. Special properties are studied for the particular case of monadic bounded commutative pseudo BE-algebras. Monadic classes of pseudo BE-algebras are investigated and it is proved that the quantifiers on bounded commutative pseudo BE-algebras are also quantifiers on the corresponding pseudo MV-algebras. The monadic deductive systems and monadic congruences of monadic pseudo BE-algebras are defined and their properties are studied. It is proved that, in the case of a monadic distributive commutative pseudo BE-algebra there is a one-to-one correspondence between monadic congruences and monadic deductive systems, and the monadic quotient pseudo BE-algebra algebra is also defined.

中文翻译：

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一元伪BE代数

摘要 在本文中，我们定义了一元伪 BE 代数并研究了它们的性质。我们证明一元伪 BE 代数的存在量词和全称量词形成残差对。针对一元有界可交换伪 BE 代数的特殊情况研究了特殊性质。研究了伪BE-代数的一元类，证明了有界可交换伪BE-代数上的量词也是相应伪MV-代数上的量词。定义了一元伪BE代数的一元演绎系统和一元同余，并研究了它们的性质。证明了在一元分配可交换伪BE代数的情况下，一元同余和一元演绎系统之间存在一一对应，