In Chajda and Länger (Math. Bohem. 143, 89–97, 2018 ) the concept of relative pseudocomplementation was extended to posets. We introduce the concept of a congruence in a relatively pseudocomplemented poset within the framework of Hilbert algebras and we study under which conditions the quotient structure is a relatively pseudocomplemented poset again. This problem is solved e.g. for finite or linearly ordered posets. We characterize relative pseudocomplementation by means of so-called L-identities. We investigate the category of bounded relatively pseudocomplemented posets. Finally, we derive certain quadruples which characterize bounded Hilbert algebras and bounded relatively pseudocomplemented posets up to isomorphism using Glivenko equivalence and implicative semilattice envelope of Hilbert algebras.

中文翻译：

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相对伪补集的代数方面

在 Chajda 和 Länger (Math. Bohem. 143, 89–97, 2018) 中，相对伪互补的概念被扩展到偏序集。我们在希尔伯特代数的框架内引入了相对赝补偏序中的同余的概念，并且我们研究了在什么条件下商结构再次是相对赝补偏序。例如，对于有限或线性有序的偏序集，该问题已解决。我们通过所谓的 L 身份来表征相对伪互补。我们研究了有界相对伪互补偏序集的类别。最后，我们使用 Glivenko 等价和 Hilbert 代数的隐含半格包络推导出某些表征有界希尔伯特代数和有界相对赝补偏序直至同构的四元组。