TENSOR MODELS AND HIERARCHY OF n-ARY ALGEBRAS

On $n$-ary Hypergroups and Fuzzy $n$-ary Homomorphism

Subdivision Depth Computation for Tensor Product n-Ary Volumetric Models

and Applied Analysis 3 P 1 2i P 1 2i 1 P 1 2i 2 P i 1 P 1 2i 3 P 1 2i 4 P k i 2 P k i a P 1 3i P 1 3i 1 P 1 3i 2 P i 1 P 1 3i 3 P 1 3i 4 P 1 3i 5 P 1 3i 6 P k i 2 P k i b P 1 4i P 1 4i 1 P 1 4i 2 P k i 1 P 1 4i 3 P 1 4i 4 P 1 4i 5 P 1 4i 6 P 1 4i 7 P 1 4i 8 P k i 2 P k i c Figure 1: Solid lines show coarse polygons whereas doted lines are refined polygons. a – c represent binary, ternary, and q...

Varieties of Anticommutative n-ary Algebras

A fundamental problem in the theory of n-ary algebras is to determine the correct generalization of the Jacobi identity. This paper describes some computational results on this problem using representations of the symmetric group. It is well known that over a field of characteristic 0 any variety of n-ary algebras can be defined by multilinear identities. In the anticommutative case, it is show...

n-ary associative algebras, cohomology, free algebras and coalgebras

When n is odd, a cohomology of type Hochschild for n-ary partially associative algebras has been defined in Gnedbaye’s thesis. Unfortunately, the cohomology definition is not valid when n is even. This fact is found again in the computations of the n-ary partially associative free algebra. In this work, we define in a first time two approachs of an Hochschild cohomology for n-ary partially asso...

NEW TYPES OF FUZZY n-ARY SUBHYPERGROUPS OF AN n-ARY HYPERGROUP

In this paper, the new notions of ``belongingness ($in_{gamma}$)"and ``quasi-coincidence ($q_delta$)"  of a fuzzy point with a fuzzyset are  introduced. By means of this new idea, the  concept of$(alpha,beta)$-fuzzy $n$-ary subhypergroup of an $n$-aryhypergroup is given, where $alpha,betain{in_{gamma}, q_{delta},in_{gamma}wedge q_{delta}, ivq}$,  andit is shown that, in 16 kinds of $(alpha,beta...