New posts in projective-module

Simple, Cyclic and Projective Modules

abstract-algebra modules homological-algebra projective-module

Free modules are projective.

abstract-algebra projective-module

Simple objects with isomorphic projective covers

category-theory abelian-categories projective-module

Prove that $M$ is a free module if and only if $M$ is a projective module over $PID$.

abstract-algebra ring-theory modules principal-ideal-domains projective-module

Modules which are isomorphic to their tensor product.

abstract-algebra commutative-algebra modules projective-module

A module is projective iff it has a projective basis

abstract-algebra modules projective-module

Finitely generated projective modules are isomorphic to their double dual.

abstract-algebra projective-module

Is every submodule of a projective module projective?

modules projective-module

Does there exist a projective module over $k[x_1,...,x_n]$ which is not free?

commutative-algebra modules projective-module

Let $R$ be an integral domain and let $X$ be a torsion module over $R$. Then $Tor_n(X,Y)$ is a torsion module for every $n≥0$.

modules homological-algebra projective-module

Every finitely generated flat module over a ring with a finite number of minimal primes is projective

commutative-algebra modules projective-module flatness

An isomorphism concerned about any finitely generated projective module

abstract-algebra modules noncommutative-algebra projective-module

Being direct summand of free module implies having dual basis.

abstract-algebra modules homological-algebra projective-module free-modules

Lemma on infinitely generated projective modules

ring-theory modules projective-module

A direct product of projective modules which is not projective

ring-theory modules homological-algebra projective-module

Show $\mathbb{Q}[x,y]/\langle x,y \rangle$ is Not Projective as a $\mathbb{Q}[x,y]$-Module.

commutative-algebra polynomials modules projective-module

What is a projective ideal?

abstract-algebra reference-request ideals projective-module

If $f:R\to S$ is an $R$-algebra and $P$ is a projective $S$-module, then $pd_R(P)\le pd_R(S)$.

homological-algebra projective-module

Semisimplicity is equivalent to each simple left module is projective?

abstract-algebra ring-theory noncommutative-algebra projective-module

Milnor Squares and Milnor Patching: Examples?

ring-theory projective-module k-theory