Is it possible to set up an ordering on a ring compatible with ring structure only if it has no proper zero divisors?
1141
Existence of totally ordered ring with zero divisors
116651
Show for any simple ring without identity, R, that R is a division ring.
91962
In a ring $a*a=0$ then $a+a=0$
105913
Calculations in quotient rings
74377
Is the natural order relation on an idempotent semiring total/linear?
67342
Why does a minimal prime ideal consist of zerodivisors?
47114
What is necessary and/or sufficient for polynomials to provide isomorphic quotient rings?
138469
Is a ring of integers necessarily Noetherian?
74441
Zero divisors in matrix rings
116916
What's the rationale for requiring that a field be a $\boldsymbol{non}$-$\boldsymbol{trivial}$ ring?
68633
Example of Noetherian ring over which the Euclidean algorithm is not valid.
120637
Is there a unique cyclic submodule for every factor dividing the order of a cyclic module?
155445
What kind of ring $R$ makes $\mathcal O(\mathrm{Proj}\,R[x_0,\cdots,x_n])=R$?
155642
Understanding divison by monic polynomial in $R[x]$ where $R$ is an arbitrary ring
3217
Construction of uncountably many non-isomorphic linear (total) orderings of natural numbers
69012
How to directly prove every element in a ring with exactly three ideals is either a unit or a zero divisor?
114254
Zero divisors in $A[x_1,x_2,\dots,x_r]$