 For example, it can be used to solve linear Diophantine equations and Chinese remainder problems for Gaussian integers; continued fractions of Gaussian integers can also be defined.A set of elements under two binary operations, denoted as addition and multiplication, is called a Euclidean domain if it forms a commutative ring and, roughly speaking, if a generalized Euclidean algorithm can be performed on them.The two operations of such a ring need not be the addition and multiplication of ordinary arithmetic; rather, they can be more general, such as the operations of a mathematical group or monoid.