In this paper, we study the lattice and the Boolean algebra, possibly closed under quotient, generated by the languages of the form u∗, where u is a word. We provide effective equational characterisations of these classes, i.e. one can decide using our descriptions whether a given regular language belongs or not to each of them.

Y. Gao et al. studied for the first time the transition complexity of Boolean operations on regular languages based on not necessarily complete DFAs. For the intersection and the complementation, tight bounds were presented, but for the union operation the upper and lower bounds differ by a factor of two. In this paper we continue this study by giving tight upper bounds for the concatenation, t...

In this paper we establish a characterization of abelian compact Hausdorff semigroups with unique idempotent and ideal retraction property. We also introduce a function algebra on a semitopological semigroup whose associated semigroup compactification is universal withrespect to these properties.

Basic results in combinatorial mathematics provide the foundation for a theory and calculus for reasoning about sequential behavior. A key concept of the theory is a generalization of Boolean implicant in which one now deals with statements of the form: A sequence of Boolean expressions α is an implicant of a set of sequences of Boolean expressions A This notion of a generalized implicant takes...

In this paper we characterize the regular medial algebras, the paramedial n-ary groupoids with a regular element, the paramedial algebras with a regular element and the regular paramedial algebras. Also, we characterize paramedial, co-medial and co-paramedial pairs of quasigroup operations and paramedial, co-medial and co-paramedial algebras with the quasigroup operations.

Let H be the real algebra of quaternions. The notion of regular function of a quaternionic variable recently presented by G. Gentili and D. C. Struppa developed into a quite rich theory. Several properties of regular quaternionic functions are analogous to those of holomorphic functions of one complex variable, although the diversity of the quaternionic setting introduces new phenomena. This pa...

In this article, we give necessary and sufficient conditions under which the Leavitt path algebra $$L_K(\mathcal {G})$$ of an ultragraph $$\mathcal {G}$$ over a field K is purely infinite simple that it von Neumann regular. Consequently, obtain every graded either locally matricial algebra, or full matrix ring $$K[x, x^{-1}]$$ , algebra.