An Abelian algebra is a mathematical structure that satisfies certain algebraic properties, including commutativity and associativity. Synonyms for Abelian algebra include commutative algebra and associative algebra. Commutative algebra is a branch of algebra that studies commutative rings, which are algebraic structures that satisfy commutative multiplication. Associative algebra is a more general term that refers to any algebraic structure satisfying associativity. Other related terms include commutative field, which is a commutative ring with multiplicative inverses, and commutative group, which is a group with a commutative operation. Overall, these synonyms reflect the different properties of Abelian algebras and the related mathematical structures.