We study the class of symmetric [Formula: see text]-ary bands. These are semigroups text] such that is invariant under action permutations and idempotent, i.e., satisfies for all text]. first provide a structure theorem these bands extends classical (strong) semilattice decomposition certain classes introduce concept strong we show exactly semilattices extensions Abelian groups whose exponents ...

A q-ary maximum distance separable (MDS) code C with length n, dimension k over an alphabet A of size q is a set of qk codewords that are elements of An, such that the Hamming distance between two distinct codewords in C is at least n− k+1. Sets of mutually orthogonal Latin squares of orders q ≤ 9, corresponding to two-dimensional q-ary MDS codes, and q-ary one-error-correcting MDS codes for q ...

applications of hypergroups have mainly appeared in special subclasses. one of the important subclasses is the class of polygroups. in this paper, we study the notions of nilpotent and solvable polygroups by using the notion of heart of polygroups. in particular, we give a necessary and sufficient condition between nilpotent (solvable) polygroups and fundamental groups.

In this paper we introduce fuzzy congruence and fuzzy strong congruence of semi-hypergroups as well as polygroups. We obtain some results in this respect. We also prove that FC(H), the set of all fuzzy strong congruences on a polygroup H , consists a complete lattice and this lattice is isomorphic to FN (H), the lattice of fuzzy normal subpolygroups.

In general, an n-ary predicate (relation) describes the relationship among its arguments, and such that no argument has to be of a special mode. The uniication and the resolution (SLDNF-resolution) do capture this state of aaair. Hence, the aim of logic programming is in some point approximatively achieved if the system is able to automatically determine the descriptive mode of an n-ary predica...

In this paper, we investigate the fault-tolerant capabilities of the k-ary n-cubes for even integer k with respect to the hamiltonian and hamiltonian-connected properties. The k-ary n-cube is a bipartite graph if and only if k is an even integer. Let F be a faulty set with nodes and/or links, and let k 3 be an odd integer. When |F | 2n−2, we show that there exists a hamiltonian cycle in a wound...