quotient ring (R/I) has multiplicative identity but R does not
91129
Can there be an onto homomorphism from a ring without unity to a ring with unity?
121465
$R[x]$ has a subring isomorphic to $R$.
155445
What kind of ring $R$ makes $\mathcal O(\mathrm{Proj}\,R[x_0,\cdots,x_n])=R$?
107821
The ring of integers of $\mathbf{Q}[i]$
77198
Showing that the characteristic of a commutative ring R without zero divisors is 0 or prime
8374
How to prove that $R/I \otimes_R M \cong M / IM$
106894
If a subring of a ring R has identity, does R also have the identity?
2458
Multiplicative group $(\mathbb R^*, ×)$ is group but $(\mathbb R, ×)$ is not group, why?
139463
Commutative integral domain does not finitely generate its field of fractions
20097
Cardinality of the quotient ring $\mathbb{Z}[x]/(x^2-3,2x+4)$
63338
Noncommutative failure of IBN: $\,R^n\cong R^m \Rightarrow n - m,$ ring $R$ with maximal ideal $I$ such that $R/I$ is not a division ring?
108955
Showing $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R},+)$
158311
What is the dimension of $R[[X]]$ where $R$ is a Noetherian ring?
119067
Basic Ring Theory Question involving the unit element
79535
Prove that $R$ is a commutative ring if $x^3=x$
144789
identify the ring $\mathbb{Z}[x]/(2x-1)$
155604
Show that $k[x,y]/(xy-1)$ is not isomorphic to a polynomial ring in one variable.