algebraic structure
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set equipped with one or more finitary operations defined on it
An algebraic structure is a set of objects paired with basic operations (like addition or multiplication) that you can perform on them. Algebraic structures matter because they provide a common framework for understanding how different mathematical systems work, making it easier to apply solutions from one area of math to another.
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In mathematics, an algebraic structure or algebraic system consists of a nonempty set A (called the underlying set, carrier set or domain), a collection of operations on A (typically binary operations such as addition and multiplication), and a finite set of identities (known as axioms) that these operations must satisfy.
An algebraic structure may be based on other algebraic structures with operations and axioms involving several structures. For instance, a vector space involves a second structure called a field, and an operation called scalar multiplication between elements of the field (called scalars), and elements of the vector space (called vectors).