This paper studies the class of automaton semigroups from two perspectives: closure under constructions, and examples of semigroups that are not automaton semigroups. We prove that (semigroup) free products of finite semigroups always arise as automaton semigroups, and that the class of automaton monoids is closed under forming wreath products with finite monoids. We also consider closure under...

In this paper, we introduce the concept of fuzzy congruences on n-ary semigroups and describe quotient n-ary semigroups by fuzzy congruences. Some isomorphism theorems about n-ary semigroups are established. Moreover, we discuss a special kind of n-ary semigroups. We also establish relationships between normal fuzzy ideals and fuzzy congruences. In particular, we prove that there exists a prese...

We study the semigroup generated by hypoelliptic Laplacian on circle and maximal bounded holomorphic extension of this semigroup. Using an orthogonal decomposition into harmonic oscillators with complex shifts, we describe domain show that boundedness in a half-plane corresponds to absolute convergence expansion eigenfunctions. This relies novel integral formula for spectral projections which a...

Let $S$ be a semitopological semigroup. The $wap-$ compactification of semigroup S, is a compact semitopological semigroup with certain universal properties relative to the original semigroup, and the $Lmc-$ compactification of semigroup $S$ is a universal semigroup compactification of $S$, which are denoted by $S^{wap}$ and $S^{Lmc}$ respectively. In this paper, an internal construction of ...

Let Q be a parameter ideal of a Noetherian local ring (R, m). The Goto number g(Q) of Q is the largest integer g such that Q : m is integral over Q. We examine the values of g(Q) as Q varies over the parameter ideals of R. We concentrate mainly on the case where dimR = 1, and many of our results concern parameter ideals of a numerical semigroup ring.

We consider linear boundary value problems for higher-order parameter-elliptic equations, where the data do not belong to classical trace spaces. employ a class of Sobolev spaces mixed smoothness that admits generalized with values in Besov negative order. prove unique solvability rough half-space and sufficiently smooth domains. As an application, we show operator related linearized Cahn–Hilli...