A variety containing EMV-algebras and Pierce sheaves of EMV-algebras

摘要

According to [11], 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 circle minus to each EMV-algebra (M; boolean OR, boolean AND, circle plus, 0), we extend its language, so that (M; boolean OR, &AND, circle plus, circle minus, 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. (C) 2020 Elsevier B.V. All rights reserved.