کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4661584 | 1633436 | 2016 | 22 صفحه PDF | دانلود رایگان |
The recent discovery that very different types of algebras have a quantale as an injective envelope is analyzed. Multi-posets are introduced as a generic structure that admits an essential embedding into a quantale, explicitly realized as a completion. Effect algebras and their non-commutative extensions, quantum B-algebras, KL-algebras, groups, and various other types of algebras are genuine multi-posets, in the sense that they determine full subcategories. Some structures like partially ordered groups or effect algebras do not carry over to the injective envelope. We provide a criterion for extendability in terms of a generalized archimedean property. Applied to non-commutative topology, multi-posets lead to a symmetric version of quantum spaces as a class of spatial quantales.
Journal: Annals of Pure and Applied Logic - Volume 167, Issue 11, November 2016, Pages 1139–1160