m-parametrizable algebras are characterized by a projectiveness property. Mathematics Subject Classification (2000): 08A99.

In this paper we consider algebraic models for stepping motors. We introduce the notion of the status of a finite groupoid and consider this notion for groupoids of stepping motor programs. Mathematics Subject Classification: 08A99

An important tool in the hyperstructure theory is the fundamental relation. The factorization of a multialgebra modulo its fundamental relation provides a functor into the category of universal algebras. The question that lead us to the results we will present is whether this functor commutes with the products. 2000 Mathematics Subject Classification: 08A05, 20N20, 08A99.

In this paper, we develop fundamental concepts required to extend the concept of group action on a set fuzzy domain. We define product and by using idea cartesian products sets. construct examples demonstrate defined concepts. also discuss properties as requisite study actions Mathematics Subject Classification (2020). 08A99, 08C05, 22F05

The present paper surveys the history of algebraic represetations of complete directed graphs, known in graph theory as tournaments, or equivalently, relational structures with a trichotomous binary relation. Essentially, two kinds of algebraizations of tournaments were studied in the literature: algebras with one binary operation (called groupoids of tournaments) and algebras with two binary o...

By left magma-$e$-magma, I mean a set containingthe fixed element $e$, and equipped by two binary operations "$cdot$", $odot$ with the property $eodot (xcdot y)=eodot(xodot y)$, namelyleft $e$-join law. So, $(X,cdot,e,odot)$ is a left magma-$e$-magmaif and only if $(X,cdot)$, $(X,odot)$ are magmas (groupoids), $ein X$ and the left $e$-join law holds.Right (and two-sided) magma-$e$-magmas are de...

We prove an analog of a lemma by Mal’tsev and deduce the following analog of a result of Rosenberg [11]: let Q be a finite poset with n elements, let k denote the k-element chain, and let h be an integer such that 2 ≤ h < n ≤ k. Consider the set of all order-preserving maps from Q to k whose image contains at most h elements, viewed as an n-ary relation μQ,h on k. Then an l-ary orderpreserving ...

A discrete event system, is a dynamical system whose state evolves in time by the occurrence of events at possibly irregular time intervals. Place-transitions Petri nets (commonly called Petri nets) are a graphical and mathematical modeling tool applicable to discrete event systems in order to represent its states evolution. Timed Petri nets are an extension of Petri nets that model discrete ev...

We provide more characterizations of varieties having a term Mal’cev modulo two functions F and G. We characterize varieties neutral in the sense of F , that is varieties satisfying R ⊆ F (R). We present examples of global operators satisfying the homomorphism property, in particular we show that many known commutators satisfy the homomorphism property. See Parts I-III [2] for unexplained notat...

An effort to initiate the subject of the title: the basic tool is the study of the abstract closed interval equipped with certain equational structures. The title is wishful thinking; there ought to be a subject that deserves the name “algebraic real analysis.” Herein is a possible beginning. For reasons that can easily be considered abstruse we were led to the belief that the closed interval—n...