If R/I is a free R-module, then I = 0.
39652
Quotient of free module
145161
Testing whether an element of a tensor product of modules is zero
126295
What is an $R$-algebra?
69384
Are the following modules free and/or isomorphic?
25039
Zero vector of a vector space
40014
A polynomial that is zero on an open set
79957
If $R$ is an infinite ring, then $R$ has either infinitely many zero divisors, or no zero divisors
98541
If a Matrix Has Only Zero as an Eigen-Value Then It Is Nilpotent
124864
A not free $\mathbb{Z}$-module
145758
Are submodules of finitely generated free modules always free?
82788
Direct summand of a free module
40705
If $M$ is an $R$-module and $I\subseteq\mathrm{Ann}(M)$ an ideal, then $M$ has a structure of $R/I$-module
125763
If $\mathrm{tr}(A)=0$, then we have $A=BC-CB?$
34520
Is $0\,\mathrm{m}$ dimensionless?
44983
Isomorphism of R-modules
7813
In a complex vector space, $\langle Tx,x \rangle=0 \implies T = 0$
102316
why $(r+I)(s+I) = rs + I$ in the quotient ring $R ?$