moduloid
A moduloid is a mathematical structure that generalizes the concept of a ring, particularly in the context of non-commutative rings and non-associative operations. The term was introduced by Jean-Louis Loday in the 1980s as a way to study non-associative algebras and their homological properties.
A moduloid consists of an abelian group (M, +) and a binary operation * : M x M -> M
a * (b + c) = (a * b) + (a * c)
(b + c) * a = (b * a) + (c * a)
These axioms ensure that the moduloid structure is compatible with the underlying abelian group structure. Moduloids
In addition to their algebraic properties, moduloids have been studied in the context of homological algebra,