An algebraic structure is a set with certain operations defined on the set.
The set may consist of numbers but may be collections of matrices, or of permutations and, the operations will depend on the elements of the set.
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An algebraic structure is a group of one or more sets together with a set of operations such that the sets are closed under the operations and are satisfying some axioms.
The rational numbers form an algebraic structure with respect to addition and this structure is called a group. And it is the property of a group that every element in it has an additive inverse.
Yes. That is the definition of an algebraic expression.
Algebraic expressions are terms that do not include an equality sign
They are two terms of an algebraic expression.
The additive identity for rational, real or complex numbers is 0.