Related papers: Autometrized Lattice Ordered Monoids
This paper introduces the concept of metric ideals in AL-monoids. We also examine the structure of AL-monoids and describe some of the properties of homomorphism and fundamentalisomorphism theorems.Additionaly we introduce and examine a…
In this paper, we study the geometry of AL-monoids by introducing the concept of metric betweeness and its properties t1, t2,, B-linearity, D-linearity, lattice betweeness, B-linearity, and Dlinearity, segments and equilateral triangles. It…
This paper pursues an investigation on groups equipped with an $L$-ordered relation, where $L$ is a fixed complete complete Heyting algebra. First, by the concept of join and meet on an $L$-ordered set, the notion of an $L$-lattice is…
We prove a representation theorem for totally ordered idempotent monoids via a nested sum construction. Using this representation theorem we obtain a characterization of the subdirectly irreducible members of the variety of semilinear…
In the present paper we introduce a lattice-ordered partial monoid structure on a suitable set of multilayer networks. We first study a kind of mappings that preserve the partial order and describe the order structure. After that we define…
We show that every finite semilattice can be represented as an atomized semilattice, an algebraic structure with additional elements (atoms) that extend the semilattice's partial order. Each atom maps to one subdirectly irreducible…
A mixed lattice is a lattice-type structure consisting of a set with two partial orderings, and generalizing the notion of a lattice. Mixed lattice theory has previously been studied in various algebraic structures, such as groups and…
We continue our studies on semilattice ordered algebras. This time we accept constants in the type of algebras. We investigate identities satisfied by such algebras and describe the free objects in varieties of semilattice ordered algebras…
The partial automorphism monoid of an inverse semigroup is an inverse monoid consisting of all isomorphisms between its inverse subsemigroups. We prove that a tightly connected fundamental inverse semigroup $S$ with no isolated nontrivial…
A notion of {\em normal submonoid} of a monoid $M$ is introduced that generalizes the normal subgroups of a group. When ordered by inclusion, the set $\mathsf{NorSub}(M)$ of normal submonoids of $M$ is a complete lattice. Joins are…
Abelian groups having partial orderings compatible with their binary operations have long been studied in the literature. In particular, lattice-ordered abelian groups constitute a universal-algebraic variety, and thus form a category which…
A subresiduated lattice ordered commutative monoid (or srl-monoid for short) is a pair $(\textbf{A},Q)$ where $\textbf{A}=(A,\wedge,\vee,\cdot,e)$ is an algebra of type $(2,2,2,0)$ such that $(A,\wedge,\vee)$ is a lattice, $(A,\cdot,e)$ is…
We study automorphic Lie algebras and their applications to integrable systems. Automorphic Lie algebras are a natural generalisation of celebrated Kac-Moody algebras to the case when the group of automorphisms is not cyclic. They are…
Given a positive definite even lattice and a commutative ring, there is a standard construction of a lattice vertex algebra over the commutative ring, and it admits a natural grading by non-negative integers. We describe the groups of…
Let $M$ be a cancellative and commutative monoid (written additively). The monoid $M$ is atomic if every non-invertible element can be written as a sum of irreducible elements (often called atoms in the literature). Weaker versions of…
We generalize free monoids by defining $k$-monoids. These are nothing other than the one-vertex higher-rank graphs used in $C^{\ast}$-algebra theory with the cardinality requirement waived. The $1$-monoids are precisely the free monoids. We…
We establish, generalizing Di Nola and Lettieri's categorical equivalence, a Morita-equivalence between the theory of lattice-ordered abelian groups and that of perfect MV-algebras. Further, after observing that the two theories are not…
We give an elementary characterization of those (abelian) semigroups $M$ that are direct limits of countable sequences of finite direct products of monoids of the form $C\cup\{0\}$ for monogenic groups $C$. This characterization involves…
We give several characterisations of groupoids determined by involutive automorphisms on semilattices of groups.
For an arbitrary partially ordered set $P$ its {\em dual} $P^*$ is built as the collection of all monotone mappings $P\to\2$ where $\2=\{0,1\}$ with $0<1$. The set of mappings $P^*$ is proved to be a complete lattice with respect to the…