Questions tagged [finite-rings]

Let $A$ be a finite unital ring and let $N$ be the set of nonunits of $A$. I want to show that if $|N|>1$ then $\sqrt{|A|}\leq |N|$. I have tried to find an injective function from $A$ to $N$, but I don't know anything about whether $A$ is…

Let $(R,+,\times)$ be a finite ring. $R^\times$ denotes the set of all invertible elements, i.e., units in $(R,\times)$. Find finite rings $(R,+,\times)$ such that for every unit $r\in R^\times\setminus\{1\}$, $r-1$ is a unit. I know that finite…

Classify all commutative rings with $1$ of order $p^3$. I only observed $1$ can have order $p,p^2,p^3$. If its $p^3$ then $\mathbb{Z}/(p^3)$. Otherwise will it be just be $\mathbb{Z}/(p^2)\times \mathbb{Z}/(p)$ and $\mathbb{Z}/(p) \times…

I have a doubt: Given $\frac{\mathbb{Z}_m [x]}{}$, where $m$ is composite and $f(x)=\prod_{i=1}^t f_i^{a_i} (x)$ (irreducible factors), can I admit $\frac{\mathbb{Z}_m [x]}{} \cong \bigoplus_{i=1} ^t \frac{\mathbb{Z}_m [x]}{

finite-rings

asked May 18 '20 at 19:48

Gustavo Terra

• 1