Abstract Finitary monads on Pos are characterized as precisely the free-algebra of varieties algebras. These classes ordered algebras specified by inequations in context. Analogously, finitary enriched characterized: here we work with coherent which means that their operations monotone.

Most work on infinitary algebras in the literature makes ample use of the axiom of choice AC (see, e.g., [10],[12],[14]). While the theory of arbitrary infinitary algebras can hardly be developed in a satisfactory manner without AC, in the case of Peano algebras (= word algebras, absolutely free algebras) many or even most of the basic results can be proved in Zermelo-Fraenkel set theory ZF wit...

A generalisation of a recent work of M. Aguiar and J.-L. Loday on quadri-algebras called tennea-algebras constructed over dendriform trialgebras is proposed. Such algebras allow the construction of nested dendriform trialgebras and are related to pre-Lie algebras, t-infinitesimal bialgebras and tBaxter operators. We also show that the augmented free t-ennea-algebra has a structure of connected ...

Free semigroup algebras are wot-closed algebras generated by n isometries with pairwise orthogonal ranges. They were introduced in [27] as an interesting class of operator algebras in their own right. The prototype algebra, obtained from the left regular representation of the free semigroup on n letters, was introduced by Popescu [45] in connection with multi-variable non-commutative dilation t...

We prove that every automorphism of the category of free Lie algebras is a semi-inner automorphism. This solves the problem 3.9 from [19] for Lie algebras.

A b s t r a c t. We investigate some properties of two varieties of algebras arising from quantum computation quasi-MV algebras and √ ′ quasi-MV algebras first introduced in [13], [12] and tightly connected with fuzzy logic. We establish the finite model property and the congruence extension property for both varieties; we characterize the quasi-MV reducts and subreducts of √ ′ quasiMV algebras...

In 2004, C. Sanza, with the purpose of legitimizing study \(n\times m\)-valued ?ukasiewicz algebras negation (or \(\mathbf{NS}_{n\times m}\)-algebras) introduced \(3 \times 3\)-valued negation. Despite various results obtained about m}\)-algebras, structure free for this variety has not been determined yet. She only a bound their cardinal number finite generators. note we describe finitely gene...