论文标题
两组的国家代数理论和MV代数的普遍状态
The two-sorted algebraic theory of states, and the universal states of MV-algebras
论文作者
论文摘要
我们介绍了一种两排代数理论，其模型是MV-Elgebras的状态，并且在一个分类等价中，它扩展了Mundici众所周知的一种，即具有（强级）单位的Abelian Lattice Group的状态。我们讨论自由国家及其与一个〜mv-elgebra的普遍状态的关系。我们阐明了这种普遍状态与晶格组仿射表示理论的关系。主要结果：任何局部有限的MV-Algebra的通用状态 - 尤其是任何布尔代数---均具有半神经代数。
We introduce a two-sorted algebraic theory whose models are states of MV-algebras and, to within a categorical equivalence that extends Mundici's well-known one, states of Abelian lattice-groups with (strong order) unit. We discuss free states, and their relation to the universal state of an~MV-algebra. We clarify the relationship of such universal states with the theory of affine representations of lattice-groups. Main result: The universal state of any locally finite MV-algebra---in particular, of any Boolean algebra---has semisimple codomain.
