کد مقاله کد نشریه سال انتشار مقاله انگلیسی ترجمه فارسی نسخه تمام متن
4661584 1344845 2016 22 صفحه PDF ندارد دانلود رایگان
عنوان انگلیسی مقاله
Multi-posets in algebraic logic, group theory, and non-commutative topology ☆
ترجمه فارسی عنوان
چند مجموعه جزئا مرتب در منطق جبری، نظریه گروه و توپولوژی غیر جابجایی پذیر
کلمات کلیدی
چند مجموعه جزئا مرتب ؛ جبر B کوانتومی ؛ Quantale؛ اتمام؛ پوشش تزریقی؛ فضای کوانتومی
08B30; 03G27; 46L85; 06F07Multi-poset; Quantum B-algebra; Quantale; Completion; Injective envelope; Quantum space
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات منطق ریاضی
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 167, Issue 11, November 2016, Pages 1139–1160
نویسندگان
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