Examples of 'finitely generated' in a sentence
Meaning of "finitely generated"
In mathematics, the term 'finitely generated' refers to a mathematical object, typically an algebraic structure or a module, that can be generated by a finite set of elements. It means that the entire structure can be constructed or obtained from a limited number of building blocks or generators. The concept of finitely generated objects is important in algebra and other branches of mathematics for studying properties and transformations
How to use "finitely generated" in a sentence
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finitely generated
Every finitely generated nilpotent group is supersolvable.
No algebraically closed group is finitely generated.
Any finitely generated residually finite group.
No uncountable group can be finitely generated.
Being a finitely generated free group.
Representation varieties of finitely generated groups.
Growth of finitely generated solvable groups.
Finite topological spaces are a special class of finitely generated spaces.
Classification of finitely generated abelian groups.
Finitely generated modules over a principal ideal domain.
Affine monoids are finitely generated.
Finitely generated module over a principal ideal domain.
Show that is also finitely generated.
Every finitely generated group is isomorphic to a quotient of a free group.
A group is locally soluble if every finitely generated subgroup is soluble.
See also
The finitely generated abelian groups can be completely classified.
The conjecture is a statement about finitely generated projective modules.
Finitely generated abelian group.
A group is coherent if every finitely generated subgroup is finitely presented.
A basic conjecture is that the pluricanonical ring is finitely generated.
Let be a finitely generated module over.
Any commutative ring is the colimit of finitely generated subrings.
A subgroup of a finitely generated group need not be finitely generated.
This follows from the classification of finitely generated abelian groups.
The concept of finitely generated space is related to this notion.
This is a key step in the classification of finitely generated abelian groups.
Be a finitely generated abelian group.
It is much more difficult to construct finitely generated infinite simple groups.
Finitely generated modules.
If is finitely presented and is finitely generated then is finitely generated.
Finitely generated ideal.
The conjecture has been proved for finitely generated abelian groups.
The structure of finitely generated abelian groups in particular is easily described.
A locally cyclic group is a group in which each finitely generated subgroup is cyclic.
Finitely generated space.
A ring is called universally catenary if any finitely generated algebra over it is catenary.
Finitely generated extension.
Repeat this n times and every finitely generated left ideal is principal.
A finitely generated group is nilpotent if and only if each of its subgroups is subnormal.
The theorem is also true for modules that are not finitely generated.
Let be a finitely generated group.
Do not confuse a finite field extension with a finitely generated field extension.
All other finitely generated infinite groups have exactly one end.
A ring is called universally catenary if all finitely generated algebras over it are catenary rings.
Finitely generated spaces are those determined by the family of all finite subspaces.
The free group on a finite set is finitely generated by the elements of that set.
Finitely generated abelian groups are completely classified and are particularly easy to work with.
A locally finite group is a group for which every finitely generated subgroup is finite.
It states that every finitely generated projective module over a polynomial ring is free.
This correspondence also works for a larger class of spaces called finitely generated spaces.
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Generated spark during metal grinding or cutting
A modified sine wave is generated by this conversion
Examples of using Finitely
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Being a finitely presentable group of finite asymptotic dimension
Markov chains with finitely many states
Being a finitely presentable group of finite cohomological dimension
