Cyclic module

In mathematics, more specifically in ring theory, a cyclic module is a module that is generated by one element over a ring. The concept is analogous to cyclic group, that is, a group that is generated by one element.

A left R-module M is called cyclic if M can be generated by a single element i.e. M = (x) = Rx = {rx | r ∈ R} for some x in M. Similarly, a right R-module N is cyclic, if N = yR for some y ∈ N.

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