Abstract The idempotents elements of the magma monoid (M (S), ) are characterized. The characterization is used to determine, when S has n elements, the number of idempotents in M (S) (also called M (n) ). A combinatorial argument is inferred and then this generalized principle is used in a larger setting, that is, analogs to the magma monoid are introduced for s -ary operations, and the generalized combinatorial principle is used to determine the number of idempotent elements in those new monomials. In addition, the kernel-cokernel decomposition of idempotents in the binary magma monoid is analyzed and its properties and relations with anticommutative and pseudo-anticommutative operations are established.
Sergio R. López-Permouth (Mon,) studied this question.