Algebraic Structure

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A non-empty set G equipped with one or more binary operations is said to be
an algebraic structure.

Suppose * is a binary operation on G.
Then (G, *) is an algebraic structure. (N,*), (1, +), (1, -) are all the algebraic structure.
Here, (R, +, .) is an algebraic structure equipped with two operations.


https://www.includehelp.com/basics/algebraic-structure-and-properties-of-structure.aspx

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In mathematics, an algebraic structure consists of a nonempty set A
(called the underlying set, carrier set or domain),
a collection of operations on A of finite arity (typically binary operations),
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).

Wiki

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In mathematics, there are many types of algebraic structures which are studied.
Abstract algebra is primarily the study of specific algebraic structures and
their properties.

Algebraic structures may be viewed in different ways,
however the common starting point of algebra texts is that an algebraic object
incorporates one or more sets with one or more binary operations or
unary operations satisfying a collection of axioms.

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Another branch of mathematics known as universal algebra studies algebraic structures in general.
From the universal algebra viewpoint, most structures can be divided into varieties
and quasivarieties depending on the axioms used.

Some axiomatic formal systems that are neither varieties nor quasivarieties,
called nonvarieties, are sometimes included among the algebraic structures by tradition.