We prove that there exists an ACD-ground theory | an equational theory deened by a set of ground equations plus the associativity and commutativity of two binary symbols and +, and the distributivity of over + | for which the word problem is undecidable.

We prove that the group of left self-distributivity, a cousin of Thompson’s group F and of Artin’s braid group B∞ that describes the geometry of the identity x(yz) = (xy)(xz), admits a bi-invariant linear ordering. To this end, we define a partial action of this group on finite binary trees that preserves a convenient linear ordering.

In this paper, projective modules over a quantale are characterized by distributivity, continuity, and adjointness conditions. It is then show that a morphism Q // A of commutative quantales is coexponentiable if and only if the corresponding Q-module is projective, and hence, satisfies these equivalent conditions.

A discrete Sugeno integral on a bounded distributive lattice L is defined as an idempotent weighted polynomial. Another possibility for axiomatization of integrals to consider compatible aggregation functions, uniquely extending the L-valued fuzzy measures. This paper aims study mentioned unique extension property concerning possible non-distributive lattices. We show that this equivalent distr...

(Received) We show that uniication modulo both-sided distributivity of the symbol on + can be reduced to AC1-uniication for all uniication problems which do not involve the + operator. Moreover, in this case, we can describe \almost all" solutions in a nite way, although there are in general innnitely many minimal solutions for such problems.

An extension of the infinite braid group B∞ exactly describes the left distributivity identities. These identities form a decidable family. The group B∞ is closely connected with the free left distributive structure with one generator, and inherits some order properties with simple topological meaning. A quick comparison algorithm for braid words is also given. The first aim of this paper is to...

We investigate weighted finite automata over strings and strong bimonoids. Such algebraic structures satisfy the same laws as semirings except that no distributivity laws need to hold. We define two different behaviors and prove precise characterizations for them if the underlying strong bimonoid satisfies local finiteness conditions. Moreover, we show that in this case the given weighted autom...

The concepts of γ-compactness, countable γ-compactness, the γ-Lindelöf property are introduced in L-topological spaces by means of γ-open L-sets and their inequalities when L is a complete DeMorgan algebra. These definitions do not rely on the structure of the basis lattice L and no distributivity in L is required.