List questions from graded-modules

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List Question

Nonzerodivisor can be chosen linear?

How to find a syzygy module is graded free module over R?

Finite Presentations on Graded $A$-modules over Noetherian rings.

Regularity of generic initial ideals: The only associated prime of $I$ containing $x_r$ is the maximal ideal.

Graded Leibniz algebras induced by some filtrations

Proving that $\deg(f) = - \infty$ iff $f=0.$

proving $\deg(fg) = \deg(f) + \deg(g)$ in a $\mathbb Z$-graded integral domain.

Good filtrations on $A_n(K)$ modules

Graded version of Quillen and Suslin's theorem (graded projectives of graded-free and finite rank modules are graded-free)

Definition of Irreducible Graded $Z_2$ Modules

Dimension of the associated graded module at an ideal

$\Omega^*(M)$ as a graded algebra over the ring of smooth functions. Is there a notion of basis?

An example of graded rings

Find the correct sign so that the equation is satisfied

Rank of a map between graded modules

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