TITLE:
Generator Sets for the Magma Monoid
AUTHORS:
Isaac Owusu-Mensah
KEYWORDS:
Generator Sets, Magma Monoids, Binary Operations, Semigroup, Monogenic Semigroups, Periodic Semigroups, Idempotents
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.16 No.1,
January
8,
2026
ABSTRACT: This paper explores the algebraic structures of the magma monoid
(
ℳ(
S
),⊲
)
, where
ℳ(
S
)
comprises all binary operations on
S
. We investigate the order and generator set of elements characterizing idempotents, almost constant operations, and units, which facilitates our analysis. A procedure for finding inverses of units is presented, along with key results on almost constant operations. Focusing on
| S |=2
and
| S |=3
, we classify the elements into various categories, determine their orders, and identify generating sets for the magma monoid. The findings inform a concise methodology for identifying the generator sets of an arbitrary element
∗∈ℳ(
S
)
.