What are the terms for the elements in the Euclidean algorithm $a = qb + r$? In a ring $R$ with a Euclidean norm $N$, given $a,b \in R$ with $b\neq 0$, there are elements $q, r$ such that $a = qb + r$.
Is there any special terminology for the elements $a,b,q,r$ in this context? For example, if we write $a = \frac{p}{q}$, then $p$ is the dividend or numerator, and $p$ is the divisor or denominator$.
It seems perhaps $b$ could be called the modulus and another number some word with the "and" suffix. Has any terminology been established?

$a = qb + r$


*

*$q$ quotient,

*$b$ divisor,

*$r$ remainder,

*$a$ dividend.
