If R/I is a free R-module, then I = 0.
47086
Quotient rings and free modules
155799
What would be an example of free module such that cardinality of linearly independent set is greater than the rank?
66451
In a ring, how do we prove that a * 0 = 0?
5022
Can a set containing $0$ be purely imaginary?
45606
Is there a bijection from [0,1] to R?
95146
Polynomial ring $R[X] $ has zero Jacobson radical, for $R$ a domain
118949
If $(Tx \mathbin{|} x) = 0$ for all $x$ then $T = 0$
69398
Rank-nullity theorem for free $\mathbb Z$-modules
43990
R is a commutative ring with $1\ne 0$ and $R^m \cong R^n$, then $m=n$
152223
If $0<r<1$ show that $r^n$ goes to $0$ as $n$ goes to 1.
114254
Zero divisors in $A[x_1,x_2,\dots,x_r]$
23641
Quotient ring of field is zero or itself.
40705
If $M$ is an $R$-module and $I\subseteq\mathrm{Ann}(M)$ an ideal, then $M$ has a structure of $R/I$-module
140340
Left and right R-modules
69384
Are the following modules free and/or isomorphic?
25039
Zero vector of a vector space
35569
Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$