量子的放大

Pub Date : 2023-10-01 DOI:10.1515/ms-2023-0082

Urmas Luhaäär

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摘要

摘要本文研究了量子的放大问题。我们证明了三个主要结果。首先，如果Q是一个可因式量子化矩阵，那么任何Q上的量子化矩阵都是Q的扩大;第二，具有单位元的量子Q上的任何单位里斯矩阵量子都是Q的扩大;第三，当且仅当两个量子具有联合放大时，它们是森田等效的。为了证明这些定理，我们使用了量子矩阵和模以及量子的森田语境。我们的主要定理及其证明与已知的幂等环的定理是平行的。

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Enlargements of Quantales

A bstract In this paper, we study the enlargements of quantales. We prove three main results. First, if Q is a factorizable quantale, then any matrix quantale over Q is an enlargement of Q ; second, any unital Rees matrix quantale over a quantale Q with an identity is an enlargement of Q ; third, two quantales are Morita equivalent if and only if they have a joint enlargement. To prove these theorems, we use quantale matrices and modules and Morita contexts of quantales. Our main theorems and their proofs are parallel to those known for idempotent rings.

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