论文标题
可计数逆的单体类别的表征
Characterizations of classes of countable Boolean inverse monoids
论文作者
论文摘要
据说有限的单体逆逆反向互动（适当嵌入）的无限无限逆副膜逆逆逆逆反向逆逆逆逆逆反向。从$ c^{\ ast} $ - 代数理论借用术语，我们说，如果上面的有限布尔值是同构成有限的直接产物，则这种布尔值是AF（大约有限的），如果有限的直接产物是有限的对称性逆向的，并且我们说的是单一的（如果是单一的），那么它是有限的（如果是单一的）。同构至有限的对称逆MONOID。我们抽象地表征了有限类型的布尔逆小型逆小膜，并且通过使用MV-elgebras，我们还表征了UHF单肌。
A countably infinite Boolean inverse monoid that can be written as an increasing union of finite Boolean inverse monoids (suitably embedded) is said to be of finite type. Borrowing terminology from $C^{\ast}$-algebra theory, we say that such a Boolean inverse monoid is AF (approximately finite) if the finite Boolean inverse monoids above are isomorphic to finite direct products of finite symmetric inverse monoids, and we say that it is UHF (uniformly hyperfinite) if the finite Boolean inverse monoids are in fact isomorphic to finite symmetric inverse monoids. We characterize abstractly the Boolean inverse monoids of finite type and those which are AF and, by using MV-algebras, we also characterize the UHF monoids.
