2 citations · 7 across the 14 of their papers we have counts for
16 papers
Representation and Embedding of Pseudo MV-algebras with Square Roots II. Closures
Anatolij Dvurečenskij, Omid Zahiri
In \cite{DvZa3}, we started the investigation of pseudo MV-algebras with square roots. In the present paper, the main aim is to continue to study the structure of pseudo MV-algebra…
Representation and Embedding of Pseudo MV-algebras with Square Roots I. Strict Square Roots
Anatolij Dvurečenskij, Omid Zahiri
In \cite{DvZa3}, we started the investigation of pseudo MV-algebras with square roots. In the present paper, we continue to study the structure of pseudo MV-algebras with square ro…
Some results on pseudo MV-algebras with square roots
Anatolij Dvurečenskij, Omid Zahiri
The paper provides a study of pseudo MV-algebras with square roots. We introduce different notions of a square root on a pseudo MV-algebra, and present their main properties. We sh…
On EMV-algebras with square roots
Anatolij Dvurečenskij, Omid Zahiri
A square root is a unary operation with some special properties. In the paper, we introduce and study square roots on EMV-algebras. First, the known properties of square roots defi…
A Variety Containing EMV-Algebras and Pierce Sheaves
Anatolij Dvurečenskij, Omid Zahiri
According to \cite{Dvz}, we know that the class of all EMV-algebras, , is not a variety, since it is not closed under the subalgebra operator. The main aim of this wo…
Morphisms on -algebras and Their Applications
Anatolij Dvurečenskij, Omid Zahiri
For a new class of algebras, called -algebras, every idempotent element determines an -algebra which is important for the structure of the -algebra. Therefore, in…
States on EMV-algebras
Anatolij Dvurečenskij, Omid Zahiri
We define a state as a -valued, finitely additive function attaining the value on an EMV-algebra, which is an algebraic structure close to MV-algebras, where the top ele…
The Loomis--Sikorski Theorem for -algebras
Anatolij Dvurečenskij, Omid Zahiri
Recently, in [DvZa], we have introduced -algebras which resemble -algebras but the top element is not guaranteed for them. For -complete -algebras, we prove an ana…
On EMV-algebras
Anatolij Dvurečenskij, Omid Zahiri
The paper deals with an algebraic extension of -algebras based on the definition of generalized Boolean algebras. We introduce a new algebraic structure, not necessarily with a…
On epicomplete -algebras
Anatolij Dvurečenskij, Omid Zahiri
The aim of the paper is to study epicomplete objects in the category of -algebras. A relation between injective -algebras and epicomplete -algebras is found, an equival…
When Lexicographic Product of Two po-Groups has the Riesz Decomposition Property
Anatolij Dvurečenskij, Omid Zahiri
We study conditions when a certain type of the Riesz Decomposition Property (RDP for short) holds in the lexicographic product of two po-groups. Defining two important properties o…
Orthocomplete Pseudo MV-algebras
Anatolij Dvurečenskij, Omid Zahiri
Pseudo -algebras are a non-commutative generalization of -algebras. The main purpose of the paper is to introduce and investigate orthocomplete pseudo -algebras. We use…
Some results on -complete lattices
Anatolij Dvurečenskij, Omid Zahiri
The paper deals with special types of -ordered set, -fuzzy complete lattices, and fuzzy directed complete posets (fuzzy s). First, a theorem for constructing monotone m…
Pseudo Equality Algebras -- Revision
Anatolij Dvurečenskij, Omid Zahiri
Recently Jenei introduced a new structure called equality algebras which is inspired by ideas of BCK-algebras with meet. These algebras were generalized by Jenei and Kóródi to pseu…
-Ordered and -Lattice Ordered Groups
R. A. Borzooei, A. Dvurečenskij, O. Zahiri
This paper pursues an investigation on groups equipped with an -ordered relation, where is a fixed complete complete Heyting algebra. First, by the concept of join and meet…
State BCK-algebras and State-Morphism BCK-algebras
R. A. Borzooei, A. Dvurečenskij, O. Zahiri
In the paper, we define the notion of a state BCK-algebra and a state-morphism BCK-algebra extending the language of BCK-algebras by adding a unary operator which models probabilis…