Exponentiation with integer exponents can be defined in any multiplicative monoid. These congruence classes are precisely the ones which have modular multiplicative inverses. The Dirichlet convolution of two multiplicative functions is again multiplicative. Multifractal systems are often modeled by stochastic processes such as multiplicative cascades. Vector spaces endowed with an additional multiplicative structure are called algebras. The algorithm is very similar to that provided above for computing the modular multiplicative inverse. This method is also very efficient to compute the multiplicative inverse of a power series. It is an example of an important arithmetic function that is neither multiplicative nor additive. The function is neither multiplicative nor additive. They are used to define models for the multiplicative fragment of intuitionistic linear logic. Totally additive is also used in this sense by analogy with totally multiplicative functions. Thus the determinant is a "multiplicative map". It is the algebra analogue of a multiplicative character of a group. The geometric or multiplicative standard deviation is formula 53. The relevance of the criterion to a multiplicative hash function is assessed here.