EMV-algebras with Quantifier and Semi-states on EMV-algebras
In this paper, we introduce and study EMVQ-algebras. We give some properties of EMVQ-algebras and prove that every EMVQ-algebra without top element can be EMVQ-embedded into an EMVQ-algebra (𝑁0, ∃0) with top element as a maximal monadic ideal of (𝑁0, ∃0). Also, every semisimple EMVQ-algebra is isomorphic to an EMV-clan with quantifier. The properties of semi-states on EMV-algebras are studied and a representation theorem on semi-state morphisms between EMValgebras is given.
Keywords: EMV-algebra, EMVQ-algebra, ideal, congruence, filter