finitely generated related queries in MathXchanger | QueryXchanger

Prove $\mathbb{C}[x,y]^{G} \cong \mathbb{C}[u,v,w]/(uv−w^{n})$

algebraic-geometry commutative-algebra finitely-generated ring-isomorphism
Updated December 11, 2018 17:20 PM

Let $A$ be an abelian finitely generated free group and $A/B$ be a torsion group. Show that $rank(A)=rank(B)$.

group-theory abelian-groups finitely-generated torsion-groups free-abelian-group
Updated December 11, 2018 04:20 AM

Index of subgroups in residually finite groups

abstract-algebra group-theory finitely-generated amenability
Updated December 03, 2018 17:20 PM

Localization of finitely generated algebra

commutative-algebra localization finitely-generated
Updated November 30, 2018 10:20 AM

Is a finitely generated metrizable group discrete?

abstract-algebra group-theory topological-groups finitely-generated locally-compact-groups
Updated November 29, 2018 13:20 PM

Let $R$ be a finitely generated subring of a number field. Is $R/I$ finite for every non-zero ideal of $R$?

number-theory commutative-algebra finitely-generated krull-dimension finite-rings
Updated November 28, 2018 23:20 PM

Prove that $\langle x,y,|x^2,y^2\rangle$ is an infinite group

finitely-generated
Updated November 21, 2018 22:20 PM

Why is the decomposition of $\operatorname{Tor}(M)$ into cyclic modules a "subset" of the decomposition of $M$?

abstract-algebra modules finitely-generated
Updated November 18, 2018 15:20 PM

Showing a Group Can Be Totally Ordered

group-theory finitely-generated well-orders
Updated November 04, 2018 23:20 PM

Prove that every finitely generated subgroup of a totally ordered group can be totally ordered.

abstract-algebra group-theory finitely-generated well-orders
Updated November 04, 2018 21:20 PM

Exists a discrete Euclidean isometry group that's not finitely generated?

group-theory euclidean-geometry isometry finitely-generated
Updated November 02, 2018 17:20 PM

The kernel of a surjective homomorphism G --> Z is finitely generated

geometric-group-theory finitely-generated
Updated October 27, 2018 14:20 PM

Exists a discrete isometry group that's not finitely generated?

group-theory hyperbolic-geometry isometry finitely-generated
Updated October 07, 2018 00:20 AM

Torsion subgroup of a finitely-generated abelian group is finite?

group-theory abelian-groups finitely-generated torsion-groups
Updated October 03, 2018 08:20 AM

Some properties of finitely generated nilpotent subgroups

group-theory finitely-generated nilpotent-groups
Updated September 27, 2018 19:20 PM

proving that $\mathbb{Z}_m\oplus \mathbb{Z}_n \cong \mathbb{Z}_d\oplus \mathbb{Z}_l $ as groups, where $l=lcm(m,n$) and $d=gcd(m,n)$

group-theory abelian-groups finitely-generated
Updated September 18, 2018 14:20 PM

Show that finitely generated cone in Hilbert space is closed.

hilbert-spaces finitely-generated convex-cone
Updated September 15, 2018 13:20 PM

Characterize Abelian Factor Group to Direct Product

group-theory abelian-groups finitely-generated direct-product
Updated August 26, 2018 08:20 AM

A group with finitely generated normal subgroup and finitely generated quotient is finitely generated itself

group-theory normal-subgroups finitely-generated
Updated August 25, 2018 12:20 PM

Show that the ring of polynomials with coefficients in a field, and in infinite variables, is not Noetherian

abstract-algebra ring-theory commutative-algebra noetherian finitely-generated
Updated August 21, 2018 03:20 AM

If $A,B,C$ are f.g. $\mathbf{Z}/p^n\mathbf{Z}$-modules and $A\oplus C\cong B\oplus C$, show $A\cong B$.

abstract-algebra commutative-algebra modules direct-sum finitely-generated
Updated August 20, 2018 01:20 AM

maximal $R$-linearly independent subset of a finitely generated module

abstract-algebra commutative-algebra modules finitely-generated
Updated August 12, 2018 22:20 PM

What interesting properties does $A^3$ have?

combinatorics group-theory big-list finitely-generated additive-combinatorics
Updated August 12, 2018 12:20 PM

Question about the classification theorem for finitely generated graded $F[t]$-modules

modules finitely-generated graded-rings graded-modules topological-data-analysis
Updated August 03, 2018 23:20 PM

Is the number of irreducible unitary representations of a finitely-generated group of a given dimension finite?

representation-theory finitely-generated
Updated July 22, 2018 15:20 PM

Test if group has amalgamated free product structure

abstract-algebra finitely-generated free-product
Updated July 06, 2018 15:20 PM

A finitely generated module with surjective homomorphism into $R^n$ implies kernel of the map is finitely generated.

modules finitely-generated
Updated July 03, 2018 04:20 AM

Identify the quotient of $\mathbb Z^3$ by a certain subgroup

abstract-algebra group-theory modules abelian-groups finitely-generated
Updated July 02, 2018 21:20 PM

Prove that $(\mathbb{Z}[x]/(x^2))^\times \cong \mathbb{Z} \times \mathbb{Z}_2.$

group-theory group-isomorphism finitely-generated
Updated June 24, 2018 22:20 PM

Groups $G$ for which every finitely generated $\mathbb{Z}G$-module is Hopfian

group-theory modules finitely-generated hopfian-groups
Updated June 17, 2018 08:20 AM

Is it always true, that $\lim_{n \to \infty} \frac{|A_n \cap H|}{|A_n|} = \frac{1}{[G:H]}$?

abstract-algebra group-theory limits finitely-generated additive-combinatorics
Updated June 15, 2018 11:20 AM

Homomorphism between free groups induced by group homomorphism of abelian groups.

group-theory abelian-groups group-homomorphism finitely-generated
Updated May 22, 2018 13:20 PM

Is the subgroup order always a multiple of it's generators order?

group-theory finite-groups permutations finitely-generated
Updated May 17, 2018 10:20 AM

surjective and injective mappings between finitely generated groups

group-theory finitely-generated
Updated May 10, 2018 03:20 AM

Finding the generator set of a group

group-theory cyclic-groups finitely-generated
Updated May 06, 2018 00:20 AM

Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$

abstract-algebra field-theory finitely-generated
Updated May 05, 2018 19:20 PM

Noether normalization: what is a finite map?

polynomials ring-theory integral-domain finitely-generated
Updated May 03, 2018 20:20 PM

Prime decomposition in a Dedekind domain

commutative-algebra modules finitely-generated dedekind-domain
Updated April 26, 2018 02:20 AM

If the $R$-module $M$ is finitely generated, but some generating set is not linearly independent, is $M$ not free?

linear-algebra abstract-algebra modules finitely-generated
Updated April 21, 2018 18:20 PM

Intersection of two ideals in a finitely generated $k$-algebra

commutative-algebra ideals finitely-generated
Updated April 16, 2018 06:20 AM

$M$ is a cyclic module if and only if it has a single invariant factor

abstract-algebra modules cyclic-groups finitely-generated
Updated April 11, 2018 03:20 AM

"Dimension inequality" preserving linear map for vector spaces

linear-algebra abstract-algebra vector-spaces linear-transformations finitely-generated
Updated April 09, 2018 21:20 PM

A minimal generating set of the Quaternions?

group-theory quaternions finitely-generated
Updated March 08, 2018 15:20 PM

Normal subset generates the group

group-theory finitely-generated
Updated February 28, 2018 09:20 AM

Complicated Proof of Free Group Generators by $n$ elements implies $\operatorname{Rank}(F) \le n$

abstract-algebra abelian-groups finitely-generated
Updated February 25, 2018 19:20 PM

I believe all groups are necessarily finitely or infinitely generated. Is that correct?

group-theory finite-groups abelian-groups finitely-generated
Updated February 24, 2018 17:20 PM

Ideal Generated by Nilpotent Elements is a Nilpotent Ideal

abstract-algebra ring-theory ideals nilpotence finitely-generated
Updated February 05, 2018 16:20 PM

Computing homology groups, algebra confusion

abstract-algebra algebraic-topology abelian-groups finitely-generated
Updated February 04, 2018 11:20 AM

Example of a module that is both finitely generated and finitely cogenerated, but not Artinian!

abstract-algebra commutative-algebra finitely-generated artinian
Updated February 02, 2018 17:20 PM

Module over integral domain, "Rank-nullity theorem", Exact Sequence

abstract-algebra modules exact-sequence integral-domain finitely-generated
Updated February 01, 2018 23:20 PM

finitely generated related issues & queries in MathXchanger