2017/10/17 by Anatolij Dvurečenskij, Dvurečenskij, Anatolij, Omid Zahiri +1
Computer Science · Decision Sciences · #06C15 #Advanced Algebra and Logic #Commutative Algebra (math.AC) #FOS: Mathematics #Fuzzy and Soft Set Theory #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.1710.06110
openalex publication_date 2017/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a new class of algebras, called EMV-algebras, every idempotent element a determines an MV-algebra which is important for the structure of the EMV-algebra. Therefore, instead of standard homomorphisms of EMV-algebras, we introduce EMV-morphisms as a family of MV-homomorphisms from MV-algebras [0,a] into other ones. EMV-morphisms enable us to study categories of EMV-algebras where objects are EMV-algebras and morphisms are special classes of EMV-morphisms. The category is closed under product. In addition, we define free EMV-algebras on a set X with respect to EMV-morphisms. If X is finite, then the free MV-algebra on X is a free EMV-algebras. For an infinite set X, the same is true introducing a so-called weakly free EMV-algebra.