2019/11/09 by Anatolij Dvurečenskij, Dvurečenskij, Anatolij, Omid Zahiri +1
Computer Science · Decision Sciences · #06C15 #06D35 #Advanced Algebra and Logic #Commutative Algebra (math.AC) #FOS: Mathematics #Fuzzy and Soft Set Theory #Rings and Algebras (math.RA) #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.1911.06625
openalex publication_date 2019/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
According to \citeDvz, we know that the class of all EMV-algebras, EMV, is not a variety, since it is not closed under the subalgebra operator. The main aim of this work is to find the least variety containing EMV. For this reason, we introduced the variety wEMV of wEMV-algebras of type (2,2,2,2,0) induced by some identities. We show that, adding a derived binary operation \ominus to each EMV-algebra (M;\vee,\wedge,⊕,0), we extend its language, so that (M;\vee,\wedge,⊕,\ominus,0), called an associated wEMV-algebra, belongs to wEMV. Then using the congruence relations induced by the prime ideals of a wEMV-algebra, we prove that each wEMV-algebra can be embedded into an associated wEMV-algebra. We show that wEMV is the least subvariety of the variety of wEMV-algebras containing EMV. Finally, we study Pierce sheaves of proper EMV-algebras.