In this paper we extend the notion of periodicity from words to labelled ordered trees. This is achieved by deening an equivalence relation on the support of the tree (the set of the nodes) and by requiring that equivalent nodes have the same label. Another requirement is that corresponding sons of equivalent nodes are equivalent too. Since the support of a k-ary tree may be described by a pree...

Finite monoids that generate monoid varieties with uncountably many subvarieties seem rare, and surprisingly, no finite monoid is known to generate a monoid variety with countably infinitely many subvarieties. In the present article, it is shown that there are, nevertheless, many finite monoids that generate monoid varieties with continuum many subvarieties; these include any finite inherently ...

We define and study the Picard group of a monoid scheme and the class group of a normal monoid scheme. To do so, we develop some ideal theory for (pointed abelian) noetherian monoids, including primary decomposition and discrete valuations. The normalization of a monoid turns out to be a monoid scheme, but not always a monoid.

We prove that the endomorphism monoid of the infinite random graph R contains as a submonoid an isomorphic copy of each countable monoid. As a corollary, the monoid of R does not satisfy any non-trivial semigroup identity. We also prove that the full transformation monoid on a countably infinite set is isomorphic to a submonoid of the monoid of R.

A new digital signature scheme in non-commutative Gaussian monoid is presented. Two algebraic structures are employed: Gaussian monoid and a certain module being compatible with a monoid. For both monoid and module, presentation and action level attributes are defined. Monoid action level is defined as monoid element (word) action on module element as an operator. A module is a set of functions...

We study a monoid associated to complex semisimple Lie algebras, called the quantic monoid. Its monoid ring is shown to be isomorphic to a degenerate quantized enveloping algebra. Moreover, we provide normal forms and a straightening algorithm for this monoid. All these results are proved by a realization in terms of representations of quivers, namely as the monoid of generic extensions of a qu...

The dual symmetric inverse monoid I ∗ n is the inverse monoid of all isomorphisms between quotients of an n-set. We give a monoid presentation of I ∗ n and, along the way, establish criteria for a monoid to be inverse when it is generated by completely regular elements.

The Catalan monoid and partial Catalan monoid of a directed graph are introduced. Also introduced is the notion of a local endomorphism of a tree, and it is shown that the Catalan (resp. partial Catalan) monoid of a tree is simply its monoid of extensive local endomorphisms (resp. partial endomorphisms) of nite shift. The main results of this paper are presentations for the Cata-lan and partial...

In this paper we define and study what we call the double Catalan monoid. This monoid is the image of a natural map from the 0-Hecke monoid to the monoid of binary relations. We show that the double Catalan monoid provides an algebraization of the (combinatorial) set of 4321-avoiding permutations and relate its combinatorics to various off-shoots of both the combinatorics of Catalan numbers and...