In this paper, we aim at highlighting the significance of the A- and B-properties introduced by Finch (Bull Aust Math Soc 2:57–62, 1970b). These conditions turn out to capture interesting structural features of lattices of closed subspaces of complete inner vector spaces. Moreover, we generalise them to the context of effect algebras, establishing a novel connection between quantum structures (orthomodular posets, orthoalgebras, effect algebras) arising from the logico-algebraic approach to quantum mechanics.

中文翻译：

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关于Finch完成正交模态集的条件

在本文中，我们旨在突出Finch引入的A和B属性的重要性（Bull Aust Math Soc 2：57-62，1970b）。这些条件证明捕获了完整内部向量空间的封闭子空间的格子的有趣结构特征。此外，我们将它们推广到效应代数的上下文中，从而建立了从量子力学的逻辑-代数方法中产生的量子结构（正模态微调子，正态代数，效应代数）之间的新型连接。