Completely multiplicative function: Difference between revisions

Revision as of 06:44, 2 November 2016

Revision as of 20:58, 9 January 2017

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Without the requirement that ''f''(1) = 1, one could still have ''f''(1) = 0, but then ''f''(''a'') = 0 for all positive integers ''a'', so this is not a very strong restriction.

The definition above can be rephrased using the language of algebra: A completely multiplicative function is a homormorphismhomomorphism from the monoid <math>(\mathbb Z^+,\cdot)</math> (that is, the positive integers under multiplication) to some other monoid.

==Examples==