A. Azarang

activity

20122026

most citedOn Fields With Only Finitely Many Maximal Subrings

4 citations · 4 across the 11 of their papers we have counts for

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5 papers · 1 filter

math.AC2023

Maximal subrings up to isomorphism of fields

Alborz Azarang, Nasrin Parsa

In this paper we study maximal subrings up to isomorphism of fields. It is shown that each field with zero characteristic has infinitely many maximal subrings up to isomorphism. If…

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.AC2014★ 4 cited

On Fields With Only Finitely Many Maximal Subrings

Alborz Azarang

Fields with only finitely many maximal subrings are completely determined. We show that such fields are certain absolutely algebraic fields and give some characterization of them.…