List questions from graded-rings

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Is every (left) graded-Noetherian graded ring (left) Noetherian?

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Definition of “degree zero” in the localization of a graded ring

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Ideal is graded iff it is generated by homogeneous elements

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what's the meaning of $B_m/f^n$?

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How does coassociativity of a coalgebra $C$ imply that the derivation on $\Omega C$ is a differential?

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Indecomposable graded $A$-modules with $\operatorname{End}_A(M)/\mathfrak m\neq k$

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When a homogeneous ideal is written as a product of two ideals, then each of two ideals is homogeneous?

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Tensor product of graded algebras 3

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Ascending / descending chain condition on graded modules.

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Isomorphism between localizations of graded ring $S_{(P)} \cong [S_{(f)}]_{PS_f \cap S_{(f)}}$

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Irreducible highest weight representations as a graded algebra

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Passing from a set of generators to a set of homogeneous generators

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Intermediate step solving Hartshorne Ex II-3.12 a)

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List Question

On the structure of $R_0$ in graded PID $R=\bigoplus_{n \ge 0} R_n$

Is every (left) graded-Noetherian graded ring (left) Noetherian?

Definition of “degree zero” in the localization of a graded ring

Ideal is graded iff it is generated by homogeneous elements

what's the meaning of $B_m/f^n$?

How does coassociativity of a coalgebra $C$ imply that the derivation on $\Omega C$ is a differential?

Indecomposable graded $A$-modules with $\operatorname{End}_A(M)/\mathfrak m\neq k$

When a homogeneous ideal is written as a product of two ideals, then each of two ideals is homogeneous?

Tensor product of graded algebras 3

Ascending / descending chain condition on graded modules.

Isomorphism between localizations of graded ring $S_{(P)} \cong [S_{(f)}]_{PS_f \cap S_{(f)}}$

Graded global sections of Proj(S) for S a polynomial ring and more general

Irreducible highest weight representations as a graded algebra

Passing from a set of generators to a set of homogeneous generators

Intermediate step solving Hartshorne Ex II-3.12 a)

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