finitely generated
The term "finitely generated" is used across various fields of mathematics to describe structures that can be entirely described by a finite set of elements.
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Definition
C2Algebra
(technical)A structure where all elements can be derived from a finite set of generators using the structure's operations.
Example
- The group is finitely generated, as every element can be expressed using a finite set of generators.
C2Ring Theory
(technical)An ideal in a ring that can be generated by a finite set of elements.
Example
- The ideal is finitely generated, meaning it can be described by a finite number of elements.
C2Module Theory
(technical)A module that has a finite set of elements such that every element in the module can be expressed as a linear combination of these generators.
Example
- Every element in this finitely generated module can be written as a combination of a finite set of generators.
C2Topology
(technical)A topological space where the topology can be defined by a finite number of open sets.
Example
- The topology of this space is finitely generated by a finite number of open sets.