A subring may have a different identity,why?
141100
Nontrivial subring with unity different from the whole ring?
148569
Embeddings $A → B → A$, but $A \not\cong B$?
34754
Why is the polynomial ring of more than one variable not a PID?
52461
Why does $(g^b \bmod m)^a \bmod m = (g^a \bmod m)^b \bmod m$?
111679
Example of a ring without unity that has a subring with unity?
40478
If $C$ commutes with certain matrices $A$ and $B$, why is $C$ a scalar multiple of the identity?
145025
Why is the partial trace of this subsystem equal to this?
13771
Why are two permutations conjugate iff they have the same cycle structure?
120495
Does this correctly interpret the "$\cong$" between groups as "$=$" between sets?
112731
If $Y$ is connected, why is $A\cup Y$ connected in this case?
150170
Subrings of fraction fields
11573
Rings and some of their properties
17059
A ring element with a left inverse but no right inverse?
83100
Prove that the center of a ring is a subring.
74139
Subrings of integral domains have the same identity element.
125174
Combinatorial intuition of identity
74924
identity element of $(D_n ,\gcd)$