Showing that a divisor of zero in a commutative ring with unity can have no multiplicative inverse"
121663
If $a$ is a zero divisor of $\mathbb{F}$, then does $a$ fail to have a multiplicative inverse?
120557
Group of invertible elements of a ring has never order $5$
154530
Rings whose elements are partitioned between units and zero-divisors.
138337
On a ring $R$ where $x^2 = x$, we must have that $2x = 0$ and $R$ is commutative
94532
How to prove a commutative, with unit, Noetherian ring $A$ only has finitely many minimal prime ideals via the following step?
38346
Commutative Ring: Nilpotent elements closed under addition?
14343
Every nonzero element in a finite ring is either a unit or a zero divisor
63568
Ring with finitely many zerodivisors
94855
Prove if a (mod n) has a multiplicative inverse, then it's unique
14055
How to show that a finite commutative ring without zero divisors is a field?
116526
Finite ring has only zero divisors and units
83255
Finding inverse in non-commutative ring
16023
Are associates unit multiples in a commutative ring with $1$?
95146
Polynomial ring $R[X] $ has zero Jacobson radical, for $R$ a domain
155642
Understanding divison by monic polynomial in $R[x]$ where $R$ is an arbitrary ring
21840
Zero divisors and units for the ring $\mathbb{Z}/n\mathbb{Z}$ with integer $n$
1686
Show that quotient rings are not isomorphic