Abstract We introduce and investigate central lifting property (CLP) for orthomodular lattices as a property whereby all central elements can be lifted modulo every p-ideal. It is shown that prime ideals, maximal ideals and finite p-ideals have CLP. Also Boolean algebras, simple chain finite orthomodular lattices, subalgebras of an orthomodular lattices generated by two elements and finite orthomodular lattices have CLP. The main results of the present paper include the investigation of CLP for principal p-ideals and finite direct products of orthomodular lattices.

中文翻译：

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正交模格的中心提升特性

摘要 我们介绍并研究了正模晶格的中心提升特性 (CLP) 作为一种特性，即所有中心元素都可以以每个 p 理想为模被提升。结果表明，素理想、极大理想和有限p理想都具有CLP。布尔代数、简单链有限正模格、由两个元素生成的正模格的子代数和有限正模格具有 CLP。本文的主要结果包括研究 CLP 的主要 p 理想和正交模格的有限直积。