满足$(2x)^2 = 2(x^2)$的对合MTL-代数的超态
Hyperstates of Involutive MTL-Algebras that Satisfy $(2x)^2 = 2(x^2)$
摘要：
MV-代数的态一直是深入研究和推广的对象。本文的目的是对完全和对合MTL-代数（简称IBP 0-代数）生成的簇中的代数的准线性半环和超态的态进行初步的研究。基于最近的一个结果表明IBP 0-代数可以由一个布尔代数、一个预线性半环和它们之间的一个适当定义的算子构成，我们对预线性半环的状态的第一次研究将支持和证明IBP 0-代数的超状态概念，并将实际表明每个这样的映射可以由其布尔骨架上的一个概率测度表示，以及适当定义的阿贝尔L群上的状态。
英文摘要：
States of MV-algebras have been the object of intensive study and attempts of generalizations. The aim of this contribution is to provide a preliminary investigation for states of prelinear semihoops and hyperstates of algebras in the variety generated by perfect and involutive MTL-algebras (IBP0-algebras for short). Grounding on a recent result showing that IBP0-algebras can be constructed from a Boolean algebra, a prelinear semihoop and a suitably defined operator between them, our first investigation on states of prelinear semihoops will support and justify the notion of hyperstate for IBP0- algebras and will actually show that each such map can be represented by a probability measure on its Boolean skeleton, and a state on a suitably defined abelian l-group.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
