A. Azarang

activity

20122020

collaborators

Showing math.ACShow all

3 papers · 1 filter

math.AC2020

Prime Avoidance Property

Alborz Azarang

Let $R$ be a commutative ring, we say that $A \subseteq S p ec (R)$ has prime avoidance property, if $I \subseteq ⋃_{P \in A} P$ for an ideal $I$ of $R$ , then the…

math.AC2020

Conch Maximal Subrings

Alborz Azarang

It is shown that if $R$ is a ring, $p$ a prime element of an integral domain $D \leq R$ with $⋂_{n = 1}^{\infty} p^{n} D = 0$ and $p \in U (R)$ , then $R$ has a conch maximal subring (see…

math.AC2015

A one-line undergraduate proof of Zariski's lemma and Hilbert's nullstellensatz

Alborz Azarang

We give an undergraduate short and simple proof for Zariski's lemma.