A cyclic module (or more specifically, a cyclic left -module over a ring ) is a module that is generated by a single element—the analogue of a cyclic group for modules.
In a left -module , the cyclic submodule generated by an element is often denoted .
Every cyclic left -module is isomorphic to a quotient module of the left-regular module over (that is, a quotient module of as a left -module).
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