Noun
algebraic structure (plural algebraic structures)
(algebra, universal algebra) Any one of the numerous types of mathematical object studied in algebra and especially in universal algebra;(more formally) a 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.
Algebraic structure and the word problem There are a number of results that relate solvability of the word problem and algebraic structure. Source: Internet