1.NounAny one of the numerous types of mathematical object studied in algebra and especially in universal algebra.
2.NounA mathematical object comprising a carrier set (aka underlying set or domain), an optional scalar set, a set of operations (typically binary operations, but otherwise each of finite arity) and a set of identities (axioms) which the operations must satisfy.
"The definition of algebraic structure establishes a framework through which to compare otherwise very different abstract objects, and to study similarities and patterns made apparent by the definition."