Let k be a subring of the field of rational functions in x, v, s which contains x, v, s. If M is an oriented 3-manifold, let S(M) denote the Homflypt skein module of M over k. This is the free k-module generated by isotopy classes of framed oriented links in M quotiented by the Homflypt skein relations: (1) xL+ − xL− = (s − s)L0; (2) L with a positive twist = (xv)L; (3) L ⊔ O = ( v−v −1 s−s−1 )...

Let k be a subring of the eld of rational functions in x; v; s which contains x 1 ; v 1 ; s 1. If M is an oriented 3-manifold, let S(M) denote the Hommypt skein module of M over k. This is the free k-module generated by isotopy classes of framed oriented links in M quotiented by the Hommypt skein relations: (1) x ?1 L + ? xL ? = (s ? s ?1)L 0 ; (2) L with a positive twist = (xv ?1)L; (3) L t O ...

We prove the following results: (1) Every group is a maximal subgroup of some free idempotent generated semigroup. (2) Every finitely presented group is a maximal subgroup of some free idempotent generated semigroup arising from a finite semigroup. (3) Every group is a maximal subgroup of some free regular idempotent generated semigroup. (4) Every finite group is a maximal subgroup of some free...

Motivated by the study of von Neumann regular skew groups as carried out by Alfaro, Ara and del Rio in [1] we investigate regular and biregular Hopf module algebras. If A is an algebra with an action by an affine Hopf algebra H, then any H-stable left ideal of A is a direct summand if and only if A is regular and the invariance functor (−) induces an equivalence of A -Mod to the Wisbauer catego...

This paper is devoted to classify all idempotent uninorms defined on the finite scale Ln = {0, 1, . . . , n}, called discrete idempotent uninorms. It is proved that any discrete idempotent uninorm with neutral element e ∈ Ln is uniquely determined by a decreasing function g : [0, e]→ [e, n] and vice versa. Based on this correspondence, the number of all possible discrete idempotent uninorms on ...

In this paper, we define hedge operation on a residuated skew lattice and investigate some its properties. We get relationships between some special sets as dense, nilpotent, idempotent, regular elements sets and their hedges.  By examples, we show that hedge of a dense element is not a dense and hedge of a regular element is not a regular. Also hedge of a nilpotent element is a nilpotent and h...

In this paper we introduce the notion of interval-valued (i.v.) fuzzy prime and semiprime ideals of a hypersemiring and study different properties of these two ideals. Finally, we examine the strongly irreducibility and irreducibility of an i.v. fuzzy ideal of a hypersemiring and characterize the equivalence of primeness, strongly irreducibility and irreducibility of an i.v. fuzzy ideal of a fu...

Previously, idempotent methods have been found to be extremely fast for solution of dynamic programming equations associated with deterministic control problems. The original methods exploited the idempotent (e.g., max-plus) linearity of the associated semigroup operator. However, it is now known that the curse-of-dimensionality-free idempotent methods do not require this linearity. Instead, it...

Considering measure theory in which the semifield of positive real numbers is replaced by an idempotent semiring leads to the notion of idempotent measure introduced by Maslov. Then, idempotent measures or integrals with density correspond to supremums of functions for the partial order relation induced by the idempotent structure. In this paper, we give conditions under which an idempotent mea...

the submodules with the property of the title ( a submodule $n$ of an $r$-module $m$ is called strongly dense in $m$, denoted by $nleq_{sd}m$, if for any index set $i$, $prod _{i}nleq_{d}prod _{i}m$) are introduced and fully investigated. it is shown that for each submodule $n$ of $m$ there exists the smallest subset $d'subseteq m$ such that $n+d'$ is a strongly dense submodule of $m$...