overArtinianRing
P73431
predicate
Indicates that the relevant algebraic structure (such as a module or algebra) is defined over, or considered with respect to, a base ring that is Artinian.
All labels observed (1)
| Label | Occurrences |
|---|---|
| overArtinianRing canonical | 2 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: overArtinianRing
Generated description
Indicates that the relevant algebraic structure (such as a module or algebra) is defined over, or considered with respect to, a base ring that is Artinian.
Sample triples (2)
| Subject | Object |
|---|---|
| Artinian module | every finitely generated module is Artinian if and only if it is Noetherian ⓘ |
| Artinian module | every module of finite length is Artinian ⓘ |