论文标题
本地半频谱
The spectrum of a localic semiring
论文作者
论文摘要
已经设计了许多频谱构建体来从代数数据中提取拓扑空间。突出的例子包括通勤环的Zariski光谱，有界分布晶格的石材光谱，可交换Unital C*-Algebra的Gelfand频谱以及连续框架的Hofmann-Lawson Spectrum。 受上面示例的启发，我们为本地半段定义了一个频谱。我们在Suplattices的对称单体类别中使用参数来证明，在上述示例满足的条件下，可以将频谱构造为公开的弱闭合根治性理想的框架，并且在这些情况下它可以减少为通常的结构。我们的证明是建设性的。 我们的方法实际上提供了“量化”频谱，然后可以得出更熟悉的本地频谱。对于离散的环，这会产生理想的量化，并且通常应包含有关半导体的其他“差异”信息。
A number of spectrum constructions have been devised to extract topological spaces from algebraic data. Prominent examples include the Zariski spectrum of a commutative ring, the Stone spectrum of a bounded distributive lattice, the Gelfand spectrum of a commutative unital C*-algebra and the Hofmann-Lawson spectrum of a continuous frame. Inspired by the examples above, we define a spectrum for localic semirings. We use arguments in the symmetric monoidal category of suplattices to prove that, under conditions satisfied by the aforementioned examples, the spectrum can be constructed as the frame of overt weakly closed radical ideals and that it reduces to the usual constructions in those cases. Our proofs are constructive. Our approach actually gives 'quantalic' spectrum from which the more familiar localic spectrum can then be derived. For a discrete ring this yields the quantale of ideals and in general should contain additional 'differential' information about the semiring.
