Multiplicative orders of elements of rings

Content created by Egbert Rijke and Gregor Perčič.

Created on 2023-09-21.
Last modified on 2025-10-31.

module ring-theory.multiplicative-orders-of-units-rings where
Imports 




Idea


The
multiplicative order
of an invertible element x of a
ring R is the order of x in the
group of multiplicative units. In other
words, it is the normal subgroup of the
group of integers consisting of
all integers k such that xᵏ ＝ 1.


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