The authors use techniques and results from the theory of generalized metric spaces to give a new, short proof that every connected, linearly ordered topological space that is a cancellative topological semigroup is metrizable, and hence embeddable in R. They also prove that every separable, linearly ordered topological space that is a cancellative topological semigroup is metrizable, so embedd...

The main aim of this paper is to study fuzzy congruences of typeB semigroups. After obtaining some properties and characterizations of fuzzy good congruences on adequate semigroups, we consider fuzzy good congruences on type-B semigroups. Finally, we prove a theorem giving equivalent conditions on fuzzy cancellative congruences of such semigroups. Mathematics Subject Classification: 06F05; 20M10

We present some special properties of inverse categories with split idempotents. First, we examine a Clifford-Leech type theorem relative to such inverse categories. The connection with right cancellative categories with pushouts is illustrated by simple examples. Finally, some basic properties of inverse categories with split idempotents and kernels are studied in terms of split idempotents wh...

We generalise existing forward and backward bisimulation minimisation algorithms for tree automata to weighted tree automata. The obtained algorithms work for all semirings and retain the time complexity of their unweighted variants for all additively cancellative semirings. On all other semirings the time complexity is slightly higher (linear instead of logarithmic in the number of states). We...

Varying methods exist for computing a presentation of a finitely generated commutative cancellative monoid.We use an algorithm of Contejean andDevie [An efficient incremental algorithm for solving systems of linear diophantine equations, Inform. andComput. 113 (1994) 143–172] to show how these presentations can be obtained from the nonnegative integer solutions to a linear system of equations. ...

In this paper, we show that the formulæ of Boolean BI cannot distinguish between some of the different notions of separation algebra found in the literature: partial commutative monoids, either cancellative or not, with a single unit or not, all define the same notion of validity. We obtain this result by the careful study of the specific properties of the counter-models that are generated by t...

We describe some connections between three different fields: combinatorics (umbral calculus), functional analysis (linear functionals and operators) and harmonic analysis (convolutions on group-like structures). Systematic usage of cancellative semigroup, their convolution algebras, and tokens between them provides a common language for description of objects from these three fields.