Birget, J.-C., SW. Margolis and J.C. Meakin, The word problem for inverse monoids presented by one idempotent relator, Theoretical Computer Science 123 (1994) 2733289. We study inverse monoids presented by a finite set of generators and one relation e= I, where e is a word representing an idempotent in the free inverse monoid, and 1 is the empty word. We show that (1) the word problem is solvab...

This paper revisits models of typed λ-calculus based on filters of intersection types: By using non-idempotent intersections, we simplify a methodology that produces modular proofs of strong normalisation based on filter models. Non-idempotent intersections provide a decreasing measure proving a key termination property, simpler than the reducibility techniques used with idempotent intersection...

In this paper we establish the existence of S-idempotents in case of loop rings ZtLn(m) for a special class of loops Ln(m); over the ring of modulo integers Zt for a specific value of t. These loops satisfy the conditions g i for every gi ∈ Ln(m). We prove ZtLn(m) has an S-idempotent when t is a perfect number or when t is of the form 2p or 3p (where p is an odd prime) or in general when t = p1...

We investigate the action of semigroups of d× d matrices with entries in the max-plus semifield on the max-plus projective space. Recall that semigroups generated by one element with projectively bounded image are projectively finite and thus contain idempotent elements. In terms of orbits, our main result states that the image of a minimal orbit by an idempotent element of the semigroup with m...

In the study of pre-Lie algebras, concept pre-morphism arises naturally as a generalization standard notion morphism. Pre-morphisms can be defined for arbitrary (not-necessarily associative) algebras over any commutative ring k with identity, and dualized in various ways to generalized morphisms (related pre-Jordan algebras) anti-pre-morphisms anti-pre-Lie algebras). We consider idempotent pre-...