Generator Sets for the Magma Monoid

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 ) .