Hyperstates of Involutive MTL-Algebras that Satisfy (2x)^2=2(x^2)

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 (IBP 0 -...

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Detalles Bibliográficos
Autores: Flaminio, Tommaso, Ugolini, Sara
Tipo de recurso: otro
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2020
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/235417
Acceso en línea:http://hdl.handle.net/10261/235417
Access Level:acceso abierto
Palabra clave:IBP 0 -algebras
Abelian ℓ -groups
Prelinear semihoop
States of prelinear semihoop
Hyperstates
Descripción
Sumario: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 (IBP 0 -algebras for short). Grounding on a recent result showing that IBP 0 -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 IBP 0 -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.