Newbetuts
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New posts in modules
A module is projective iff it has a projective basis
abstract-algebra
modules
projective-module
Is every commutative ring having the invariant basis number property equivalent to AC?
abstract-algebra
ring-theory
set-theory
modules
axiom-of-choice
If M+N and M$\cap$N are finitely generated modules, so are M and N.
abstract-algebra
modules
$2 \otimes_{R} 2 + x \otimes_{R} x$ is not a simple tensor in $I \otimes_R I$
abstract-algebra
modules
tensor-products
$k[x]/(x^n)$ module with finite free resolution is free
commutative-algebra
modules
Prove $(2, x)$ is not a free $R$-module.
linear-algebra
modules
Solutions of homogeneous linear differential equations are a special case of structure theorem for f.g. modules over a PID
abstract-algebra
ordinary-differential-equations
modules
$R$ module homomorphisms between two modules
abstract-algebra
modules
A ring that is left Noetherian but not right noetherian
ring-theory
modules
noetherian
Find kernel of induced map after tensoring
abstract-algebra
modules
tensor-products
How to show fraction field is flat (without localization)
abstract-algebra
ring-theory
modules
homological-algebra
Is every submodule of a projective module projective?
modules
projective-module
Basic exercise on localization of modules
abstract-algebra
commutative-algebra
modules
An $R$ module and $S$ module that cannot be an $R$-$S$ bimodule
commutative-algebra
ring-theory
modules
Part of the third Isomorphism theorem for modules
abstract-algebra
modules
Definition of intersection multiplicity in Hartshorne VS Fulton for plane curves
algebraic-geometry
modules
definition
algebraic-curves
intersection-theory
What does it mean that "the action of $\mathbb{Z}$ on $M$ factors through the quotient $\mathbb{Z}/p^n \mathbb{Z}$"?
number-theory
commutative-algebra
modules
abelian-groups
group-actions
Does there exist a projective module over $k[x_1,...,x_n]$ which is not free?
commutative-algebra
modules
projective-module
Injective Modules Motivation & Intuition
ring-theory
commutative-algebra
modules
injective-module
Corollary of the Malgrange Preparation Theorem
real-analysis
analysis
modules
dynamical-systems
germs
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