Explain why in a ring the additive neutral can not have a multiplicative inverse.
125604
Proof that $\mathbb{Z}$ has no zero divisors
146276
Is there a ring such that the nilradical of it is not nilpotent?
73689
A question about the equivalence relation on the localization of a ring.
158426
Proving lemma about centrality of idempotent elements in a Ring with no nilpotent elements.
52081
Why is not the ring $\mathbb{Z}[2\sqrt{2}]$ a unique factorization domain?
155642
Understanding divison by monic polynomial in $R[x]$ where $R$ is an arbitrary ring
18361
Does the unit generate the additive group in a unital ring with cyclic additive group?
76547
Why are addition and multiplication commutative, but not exponentiation?
125719
Multiplicative inverse of a complex number.
25159
Why does the inverse of the Hilbert matrix have integer entries?
116916
What's the rationale for requiring that a field be a $\boldsymbol{non}$-$\boldsymbol{trivial}$ ring?
113572
Are all multiplicative functions additive?
6646
A (non-artificial) example of a ring without maximal ideals
66451
In a ring, how do we prove that a * 0 = 0?
70610
Why is ring addition commutative?
99037
Prove the sum of all numbers that do not have a multiplicative inverse mod $n$
153291
Why a ring homomorphism from a local ring will not map a non-unit to a unit？