On the $n$-ary algebras, semigroups and their universal covers

Abstract

For any $n$-ary associative algebra we construct a ${\mathbb{Z}}_{n-1}$ graded algebra, which is a universal object containing the $n$-ary algebra as a subspace of elements of degree 1. Similar construction is carried out for semigroups.

10 pages, Uses AMS-LaTeX and XYpic