Abstract :
We introduce the class of n-perfect GMV-algebras. Such algebras can be split into n+1 comparable slices. We present an equational base for the variety generated by n-perfect GMV-algebras.
We define the category of strong n-perfect GMV-algebras and we show that every strong n-perfect GMV-algebra is always an interval in a lexicographical product of with an ℓ-group. We prove that the variety generated by strong n-perfect GMV-algebras is generated by a one strong n-perfect GMV-algebra.
Keywords :
Unital ?-group , GMV-algebra , Representation , n-perfect GMV-algebra , Strong n-perfect GMV-algebra , Categorical equivalence , variety , Top variety , state , Perfect GMV-algebra
