$R$ is a ring. $\forall 0\ne a\in R \exists ! b\in R; aba=a$. Can I conclude that $R$ is a ring with identity? How?
125661
Two problems about rings.
58532
If $M$ is an Artinian $R$-module then $R/\mbox{ann}(M)$ is an Artinian ring?
81296
If A and B are ideals of a ring, show that A + B = $\{a+b|a \in A, b \in B\}$ is an ideal
154495
Prove that a nontrivial subring of a ring that is a domain has the same identity
151803
Prove that $R$ is commutative
51593
Every finite commutative ring with no zero divisors contains a multiplicative identity?
46843
A ring without the Invariant Basis Number property
144442
Let $R$ be a commutative unital ring. Is it true that the group of units of $R$ is not isomorphic with the additive group of $R$?
1315
Let $R$ be a ring. Define a circle composition ◦ in R by $a ◦ b =a+b-ab$, $a, b ∈ R$.
29600
What is true for a ring with exactly two right ideals
73689
A question about the equivalence relation on the localization of a ring.
69012
How to directly prove every element in a ring with exactly three ideals is either a unit or a zero divisor?
127418
If ring $B$ is integral over $A$, then an element of $A$ which is a unit in $B$ is also a unit in $A$.
83100
Prove that the center of a ring is a subring.
16023
Are associates unit multiples in a commutative ring with $1$?
158311
What is the dimension of $R[[X]]$ where $R$ is a Noetherian ring?
124672
Let $f:R\rightarrow S$ be a ring homomorphism. Prove or disprove: if $f$ is onto and $R$ is an integral domain, then $S$ is an integral domain