In this paper we generalize Robinson's version of an order cancellation law in which some unbounded subsets a vector space are cancellative elements. We introduce the notion weakly narrow sets normed spaces, study their properties and prove where canceled set is narrow. Also, for closed convex topological has bounded Hausdorff-like distance from its recession cone. topologically embed semigroup...

Given a binary relation IE ∪ IR on the set of ground terms over some signature, we define an abstract rewrite closure for IE ∪ IR. An abstract rewrite closure can be interpreted as a specialized ground tree transducer (pair of bottom-up tree automata) and can be used to efficiently decide the reachability relation →IE∪IE−∪IR. It is constructed using a completion like procedure. Correctness is e...

In this contribution the Myhill-Nerode congruence relation on tree series is reviewed and a more detailed analysis of its properties is presented. It is shown that, if a tree series is deterministically recognizable over a zero-divisor free and commutative semiring, then the Myhill-Nerode congruence relation has finite index. By [Borchardt: Myhill-Nerode Theorem for Recognizable Tree Series. LN...

Let M be a commutative cancellative atomic monoid. We consider the behavior of the asymptotic length functions ̄̀(x) and L̄(x) on M . If M is finitely generated and reduced, then we present an algorithm for the computation of both ̄̀(x) and L̄(x) where x is a nonidentity element of M . We also explore the values that the functions ̄̀(x) and L̄(x) can attain when M is a Krull monoid with torsion diviso...

The concept of strong spined product of semigroups is introduced. We first show that a semigroup S is a rpp-semigroup with left central idempotents if and only if S is a strong semilattice of left cancellative right stripes. Then, we show that such kind of semigroups can be described by the strong spined product of a C-rpp-semigroup and a right normal band. In particular, we show that a semigro...