# 5.5 Operations for Ring Elements

The following operations are always available for ring elements. Of course the operands must lie in compatible rings, i.e., the rings must be equal, or at least have a common superring.

`r + s`

The operator `+` evaluates to the sum of the two ring elements r and s, which must lie in compatible rings.

`r - s`

The operator `-` evaluates to the difference of the two ring elements r and s, which must lie in compatible rings.

`r * s`

The operator `*` evaluates to the product of the two ring elements r and s, which must lie in compatible rings.

`r ^ n`

The operator `^` evaluates to the n-th power of the ring element r. If n is a positive integer then `r^n` is `r*r*..*r` (n factors). If n is a negative integer `r^n` is defined as 1 / {<r>^{-<n>}}. If 0 is raised to a negative power an error is signalled. Any ring element, even 0, raised to the 0-th power yields 1.

For the precedence of the operators see Operations.

Note that the quotient operator `/` usually performs the division in the quotient field of the ring. To compute a quotient in a ring use the function `Quotient` (see Quotient).

GAP 3.4.4
April 1997