Let T(X) be the full transformation semigroup on a set X, and let L(V) under composition of all linear transformations vector space V over field. For subset Y X subspace W V, consider semigroups $${\overline{T}}(X, Y) = \{f\in T(X):Yf \subseteq Y\}$$ $${\overline{L}}(V, W) L(V):Wf W\}$$ composition. We describe unit-regular elements in Y)$$ W)$$ . Using these, we determine when are unit-regular...

In this paper, a new definition of accepting networks – called target based accepting networks – is given. In a target based accepting network of evolutionary processors, each node is equipped with a regular language – the target set. As soon as a node contains a word of its target set, the input word is accepted by the network. In this way, no further output nodes are necessary. It is shown th...

We prove that two semigroups with local units are Morita equivalent if and only if they have a joint enlargement. This approach to Morita theory provides a natural framework for understanding McAlister’s theory of the local structure of regular semigroups. In particular, we prove that a semigroup with local units is Morita equivalent to an inverse semigroup precisely when it is a regular locall...

The upper and lower uniform densities of some regular sequences are computed. These densities are used to determine sets of sampling and interpolation for Bergman spaces of the unit disk. §

In 1995, Camillo and Yu showed that an exchange ring has stable range 1 if and only if every regular element is unit regular. An element m in a module RM is called regular if (mλ)m = m for some λ ∈ hom(M,R). In this paper we define stable modules and show that if M has the finite exchange property then M is stable if and only if, for every regular element m ∈ M, (mγ)m = m where γ : M → R is epi...

We perform an exhaustive search for the minimum 4-regular unit distance graph resulting in a lower bound of 34 vertices.