A. Azarang

activity

20122020

collaborators

4 papers

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.

math.RA2012

Submaximal Integral Domains

A. Azarang

It is proved that if $D$ is a $U F D$ and $R$ is a $D$ -algebra, such that $U (R) \cap D \neq = U (D)$ , then $R$ has a maximal subring. In particular, if $R$ is a ring which either contains…