Algebraic operation

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In mathematics,
a basic algebraic operation is any one of the common operations of arithmetic,
which include addition, subtraction, multiplication, division,
raising to an integer power, and taking roots (fractional power).[1][2]

These operations may be performed on numbers,
in which case they are often called arithmetic operations.
They may also be performed, in a similar way, on variables, algebraic expressions,[3]
and more generally, on elements of algebraic structures,
such as groups and fields.[4]

An algebraic operation may also be defined simply as a function from
a Cartesian power of a set to the same set.[5]

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Algebraic operation
Operation of ordinary algebra: that is, the arithmetical operations addition, subtraction, multiplication and division.

Operations that involve infinite series and functions such as log x are not algebraic –
they depend on the use of limits.

The term algebraic is also applied to arithmetical operations carried out with due regard to sign.
Thus, the algebraic sum of a and −b is a − b,
the algebraic product of −a and −b is +ab, etc.

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