Acceptable ring

In mathematics, an acceptable ring is a generalization of an excellent ring, with the conditions about regular rings in the definition of an excellent ring replaced by conditions about Gorenstein rings. Acceptable rings were introduced by {{harvtxt|Sharp|1977}}.

All finite-dimensional Gorenstein rings are acceptable, as are all finitely generated algebras over acceptable rings and all localizations of acceptable rings.

References

  • {{citation|mr=0441957

|last=Sharp|first= Rodney Y.

|title= Acceptable rings and homomorphic images of Gorenstein rings

|journal = Journal of Algebra

|volume = 44

|year = 1977

|pages= 246–261

|doi=10.1016/0021-8693(77)90180-6

|doi-access= free

}}

Category:Commutative algebra

Category:Ring theory

{{commutative-algebra-stub}}