Show that if $a\in R$ is not a zero divisor, then $a$ is unit.
69012
How to directly prove every element in a ring with exactly three ideals is either a unit or a zero divisor?
82953
In a ring with no zero-divisors, for $(m,n) =1$, $a^m = b^m$ and $a^n = b^n$ $\iff a =b$
87946
Proving that the unities of a ring form a group under multiplication
114813
Proof: in $\mathbb{R}$, $((0,1),|\cdot|)$ is not compact.
126821
Let $f:[0,1]\to \mathbb{R}$. Show that $\{a \in [0,1]: f(a)\neq 0\} = \bigcup_{n=1}^{\infty} \{a \in [0,1]: |f(a)|\geq 1/n\}$
62208
If $A$ is a non-empty set, then $A \notin A$
42809
How can we show that $(I-A)$ is invertible?
121663
If $a$ is a zero divisor of $\mathbb{F}$, then does $a$ fail to have a multiplicative inverse?
32929
Questions about proving $\lnot \lnot a = a$
84301
Showing that some Function on the Unit Disc is injective
127169
Show that the zeros of $\sum_{k=1}^n kz^{k-1}$ are inside the unit disc
72313
Show that for all real numbers $a$ and $b$, $\,\, ab \le (1/2)(a^2+b^2)$
78873
How to show that the monomials are not a Schauder basis for $C[0,1]$
80551
Find Units in $\mathbb{Z}[\sqrt{n}]$
91180
Show $R \setminus S$ is a union of prime ideals
29452
Divisor in $\mathbb{C}[X]$ $\implies$ divisor in $\mathbb{R}[X]$?
80735
Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact