(N + 1) - bounded Wajsberg Algebras with a U-operator

Wajsberg algebras are just a reformulation of Chang $MV-$algebras where implication is used instead of disjunction. $MV-$algebras were introduced by Chang to prove the completeness of the infinite-valued {\L}ukasiewicz propositional calculus. Bounded Wajsberg algebras are equivalent to bounded $MV-$algebras. The class of (n+1)-bounded Wajsberg algebras endowed with a $U-$operator, which plays the role of the universal quantifier, is studied. The simple algebras and the subalgebras of the finite simple algebras are characterized. It is proved that this variety of algebras is semisimple and locally finite.