Property: (right/left) coherent
Definition: (right coherent) Every finitely generated right ideal is finitely presented
Reference(s):
- T.-Y. Lam. Lectures on modules and rings. (2012) @ Section 4G
Metaproperties:
This property has the following metaproperties
- Morita invariant
- passes to matrix rings
- passes to $eRe$ for any full idempotent $e$
This property
does not have the following metaproperties
- passes to polynomial rings
(Counterexample: $R_{ 104 }$)
- passes to quotient rings
(counterexample needed)