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Engel BCI-algebras: an application of left and right commutators

Ardavan Najafi, Arsham Borumand Saeid (2021)

Mathematica Bohemica

We introduce Engel elements in a BCI-algebra by using left and right normed commutators, and some properties of these elements are studied. The notion of n -Engel BCI-algebra as a natural generalization of commutative BCI-algebras is introduced, and we discuss Engel BCI-algebra, which is defined by left and right normed commutators. In particular, we prove that any nilpotent BCI-algebra of type 2 is an Engel BCI-algebra, but solvable BCI-algebras are not Engel, generally. Also, it is proved that...

Enriched MV-algebras.

Ulrich Höhle (1995)

Mathware and Soft Computing

This paper introduces the structure of enriched MV-algebras and studies on this basis various relations between sigma-complete MV-algebras and T-tribes.

Entropy on effect algebras with the Riesz decomposition property I: Basic properties

Antonio Di Nola, Anatolij Dvurečenskij, Marek Hyčko, Corrado Manara (2005)

Kybernetika

We define the entropy, lower and upper entropy, and the conditional entropy of a dynamical system consisting of an effect algebra with the Riesz decomposition property, a state, and a transformation. Such effect algebras allow many refinements of two partitions. We present the basic properties of these entropies and these notions are illustrated by many examples. Entropy on MV-algebras is postponed to Part II.

Epimorphisms between finite MV-algebras

Aldo V. Figallo, Marina B. Lattanzi (2017)

Mathematica Bohemica

MV-algebras were introduced by Chang to prove the completeness of the infinite-valued Łukasiewicz propositional calculus. Recently, algebraic theory of MV-algebras has been intensively studied. Wajsberg algebras are just a reformulation of Chang MV-algebras where implication is used instead of disjunction. Using these equivalence, in this paper we provide conditions for the existence of an epimorphism between two finite MV-algebras A and B . Specifically, we define the mv-functions with domain in...

Equational spectrum of Hilbert varieties

R. Padmanabhan, Sergiu Rudeanu (2009)

Open Mathematics

We prove that an equational class of Hilbert algebras cannot be defined by a single equation. In particular Hilbert algebras and implication algebras are not one-based. Also, we use a seminal theorem of Alfred Tarski in equational logic to characterize the set of cardinalities of all finite irredundant bases of the varieties of Hilbert algebras, implication algebras and commutative BCK algebras: all these varieties can be defined by independent bases of n elements, for each n > 1.

Équilibre, équivalence, ordre et préordre à distance minimum d'un graphe complet

G. Ribeill (1973)

Mathématiques et Sciences Humaines

Les problèmes que nous traitons ici sont en partie familiers aux lecteurs de la revue. L'apport original consiste selon nous dans le fait d'avoir rapproché des problèmes classiques (équilibre d'un graphe, ordre à distance minimum) pour en souligner les analogies profondes et, du coup, plonger de manière féconde ces problèmes dans un ensemble plus large, en particulier en posant le problème de l'équivalence et du préordre à distance minimum d'un graphe complet. Notre exposé se présente donc comme...

Equimorphism invariants for scattered linear orderings

Antonio Montalbán (2006)

Fundamenta Mathematicae

Two linear orderings are equimorphic if they can be embedded in each other. We define invariants for scattered linear orderings which classify them up to equimorphism. Essentially, these invariants are finite sequences of finite trees with ordinal labels. Also, for each ordinal α, we explicitly describe the finite set of minimal scattered equimorphism types of Hausdorff rank α. We compute the invariants of each of these minimal types..

Equimorphy in varieties of distributive double p -algebras

Václav Koubek, Jiří Sichler (1998)

Czechoslovak Mathematical Journal

Any finitely generated regular variety 𝕍 of distributive double p -algebras is finitely determined, meaning that for some finite cardinal n ( 𝕍 ) , any subclass S ⊆ 𝕍 of algebras with isomorphic endomorphism monoids has fewer than n ( 𝕍 ) pairwise non-isomorphic members. This result follows from our structural characterization of those finitely generated almost regular varieties which are finitely determined. We conjecture that any finitely generated, finitely determined variety of distributive double p -algebras...

Equimorphy in varieties of double Heyting algebras

V. Koubek, J. Sichler (1998)

Colloquium Mathematicae

We show that any finitely generated variety V of double Heyting algebras is finitely determined, meaning that for some finite cardinal n(V), any class 𝒮 ⊆ V consisting of algebras with pairwise isomorphic endomorphism monoids has fewer than n(V) pairwise non-isomorphic members. This result complements the earlier established fact of categorical universality of the variety of all double Heyting algebras, and contrasts with categorical results concerning finitely generated varieties of distributive...

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