In this paper, first we define the notion of involutive operator on bounded involutive equality algebras and by using it, we introduce a new class of equality algebras that we called it a tense like equality algebra. Then we investigate some properties of tense like equality algebra. For two involutive bounded equality algebras and an equality homomorphism between them, we prove that the tense ...

In this paper, we introduce the notions of $(odot, oplus)$-derivations and $(ominus, odot)$-derivations for $MV$-algebras and discuss some related results. We study the connection between these derivations on an $MV$-algebra $A$ and the derivations on its boolean center. We characterize the isotone $(odot, oplus)$-derivations and prove that $(ominus, odot)$-derivations are isotone. Finally we d...

In the present paper we define the (pseudo) MV-algebras with n-ary operators, generalizing MV-modules and product MV-algebras. Our main results assert that there are bijective correspondences between the operators defined on a pseudo MV-algebra and the operators defined on the corresponding `-group. We also provide a categorical framework and we prove the analogue of Mundici’s categorical equiv...

The varietyMV of all MV-algebras is shown to be non-canonical in a strong sense. Specifically it is shown that the canonical extension of the Chang algebra, K2, is not an MV-algebra. As a consequence, no non-finitely generated variety of MV-algebras is canonical.

We present a uniform version of Di Nola Theorem, this enables to embed all MV-algebras of a bounded cardinality in an algebra of functions with values in a single non-standard ultrapower of the real interval [0, 1]. This result also implies the existence, for any cardinal α, of a single MValgebra in which all infinite MV-algebras of cardinality at most α embed. Recasting the above construction ...

In this paper, we continue our study on HvMV-algebras. The quotient structure of an HvMV-algebra by a suitable types of congruences is studied and some properties and related results are given. Some homomorphism theorems are given, as well. Also, the fundamental HvMV-algebra and the direct product of a family of HvMV-algebras are investigated and some related results are obtained.

Several algebraic structures (namely HW, BZMV , Stonean MV and MV∆ algebras) related to many valued logical systems are considered and their equivalence is proved. Four propositional calculi whose Lindenbaum– Tarski algebra corresponds to the four equivalent algebraic structures are axiomatized and their semantical completeness is given.