کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5771809 | 1630423 | 2017 | 34 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A Kochen-Specker theorem for integer matrices and noncommutative spectrum functors
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We investigate the possibility of constructing Kochen-Specker uncolorable sets of idempotent matrices whose entries lie in various rings, including the rational numbers, the integers, and finite fields. Most notably, we show that there is no Kochen-Specker coloring of the nÃn idempotent integer matrices for nâ¥3, thereby illustrating that Kochen-Specker contextuality is an inherent feature of pure matrix algebra. We apply this to generalize recent no-go results on noncommutative spectrum functors, showing that any contravariant functor from rings to sets (respectively, topological spaces or locales) that restricts to the Zariski prime spectrum functor for commutative rings must assign the empty set (respectively, empty space or locale) to the matrix ring Mn(R) for any integer nâ¥3 and any ring R. An appendix by Alexandru Chirvasitu shows that Kochen-Specker colorings of idempotents in partial subalgebras of M3(F) for a perfect field F can be extended to partial algebra morphisms into the algebraic closure of F.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 491, 1 December 2017, Pages 280-313
Journal: Journal of Algebra - Volume 491, 1 December 2017, Pages 280-313
نویسندگان
Michael Ben-Zvi, Alexander Ma, Manuel Reyes, Alexandru Chirvasitu,