A subresiduated lattice ordered commutative monoid (or srl-monoid for short) is a with particular subalgebra which contains residuated implication. The srl-monoids can be regarded as algebras that generalize lattices and respectively. In this paper we prove the class of forms variety. We show congruences any isomorphic to its strongly convex subalgebras also give description generated by subset...

Complete lattices and closure operators in ordered sets are considered from the point of view of fuzzy logic. A typical example of a fuzzy order is the graded subsethood of fuzzy sets. Graded subsethood makes the set of all fuzzy sets in a given universe into a completely lattice fuzzy ordered set (i.e. a complete lattice in fuzzy setting). Another example of a completely lattice fuzzy ordered ...

The algebraic structure of groups is familiar to anyone who has studied abstract algebra. Familiar to anyone who has studied any mathematics is the concept of ordering, for example the standard less than or equal to with the integers. We can combine these structures to create a new hybrid algebraic structure. In the following, we will define exactly how order structures and group structures int...

A lattice-ordered group (/-group) is said to be regular il no positive element of the group is disjoint from any of its conjugates. It is well known that every simple regular /-group is totally ordered [S]. The subgroups of the reals are the most elementary examples of regular simple /-groups; other examples can be found in [2] and [ó]. In this note we investigate a class of simple /-groups at ...

A metastable phase of NbN with superconducting T c =16.4 K was reported recently by Treece and collaborators. The reported structure of the thin film sample deviates from the rocksalt (B1) NbN structure with 25% ordered vacancies on each sublattice (space group Pm3m) and a lattice constant of 4.442Å. Using full potential electronic structure methods, we contrast the electronic structure with th...

The lattice of ordered compactifications of a topological sum of a finite number of totally ordered spaces is investigated. This investigation proceeds by decomposing the lattice into equivalence classes determined by the identification of essential pairs of singularities. This lattice of equivalence classes is isomorphic to a power set lattice. Each of these equivalence classes is further deco...

We show that for every infinite cardinal number m there exist two totally ordered abelian groups whose free product in any nontrivial variety of lattice-ordered groups has a disjoint set of cardinality m. This answers problem 10.7 of [13] and extends the results in [12]. We further prove that for the variety of abelian lattice-ordered groups or the variety of all lattice-ordered groups, the fre...

Following our recent conjecture to model the phenomenona of antiferromagnetism and superconductivity by quantum symmetry groups, we discuss in the present note the choice of the classical symmetry group underlying the quantum group. Keeping in mind the degrees of freedom arising from spin, charge, and lattice we choose the classical group as SO(7). This choice is also motivated to accomodate th...

This paper focuses on the relationship between an $L$-subset and the system of level-elements induced by it, where the underlying lattice $L$ is a complete residuated lattice and the domain set of $L$-subset is an $L$-partially ordered set $(X,P)$. Firstly, we obtain the sufficient and necessary condition that an $L$-subset is represented by its system of level-elements. Then, a new representat...