The LV-hyperstructures

The largest class of hyperstructures is the one which satisfy the weak properties and they are called H v -structures introduced in 1990. The H v(c)-structures have a partial order (poset) on which gradations can be defined. We introduce the LV-construction based on the Levels Variable

Atomistic subsemirings of the lattice of subspaces of an algebra

Let A be an associative algebra with identity over a field k. An atomistic subsemiring R of the lattice of subspaces of A, endowed with the natural product, is a subsemiring which is a closed atomistic sublattice. When R has no zero divisors, the set of atoms of R is endowed with a multivalued product. We introduce an equivalence relation on the set of atoms such that the quotient set with the induced product is a monoid, called the condensation monoid. Under suitable hypotheses on R, we show that this monoid is a group and the class of k1_A is the set of atoms of a subalgebra of A called the focal subalgebra. This construction can be iterated to obtain higher condensation groups and focal subalgebras. We apply these results to G-algebras for G a group; in particular, we use them to define new invariants for finite-dimensional irreducible projective representations.Comment: 14 page

ENLARGED FUNDAMENTALLY VERY THIN H v -STRUCTURES Communicated by B. Davvaz

Abstract. We study a new class of Hv-structures called Fundamentally Very Thin. This is an extension of the well known class of the Very Thin hyperstructures. We present applications of these hyperstructures

Roughness in n-ary hypergroups,

Abstract -In this paper the class of n-ary hypergroups is introduced and several properties are found and examples are presented. n-ary hypergroups are a generalization of hypergroups in the sense of Marty. On the other hand, we can consider n-ary hypergroups as a good generalization of n-ary groups. We define the fundamental relation * β on an n-ary hypergroup H as the smallest equivalence relation such that * / H β is the n-ary group, and then some related properties are investigated

WEAK HYPERSTRUCTURES ON SMALL SETS

The class of the weak hyperstructures is larger than the known ones originated from the hypergroup in the sense of Marty. The weak hyperstructures are also called -structures. In this paper we deal with some classes ofH,-groups defined on sets with three elements