The theory of extensive categories determines in particular the notion of separable MV-algebra (equivalently, of separable unital lattice-ordered Abelian group). We establish the following structure theorem: An MV-algebra is separable if, and only if, it is a finite product of algebras of rational numbers—i.e., of subalgebras of the MV-algebra [0,1] \cap Q. Beyond its intrinsic algebraic interest, this research is motivated by the long-term programme of developing the algebraic geometry of the opposite of the category of MV-algebras, in analogy with the classical case of commutative K-algebras over a field K.
Separable MV-algebras and lattice-ordered groups / V. Marra, M. Menni. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - 646:(2024 May 15), pp. 66-99. [10.1016/j.jalgebra.2024.01.037]
Separable MV-algebras and lattice-ordered groups
V. Marra
Primo
;
2024
Abstract
The theory of extensive categories determines in particular the notion of separable MV-algebra (equivalently, of separable unital lattice-ordered Abelian group). We establish the following structure theorem: An MV-algebra is separable if, and only if, it is a finite product of algebras of rational numbers—i.e., of subalgebras of the MV-algebra [0,1] \cap Q. Beyond its intrinsic algebraic interest, this research is motivated by the long-term programme of developing the algebraic geometry of the opposite of the category of MV-algebras, in analogy with the classical case of commutative K-algebras over a field K.File | Dimensione | Formato | |
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