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

collaborators

12 papers

math.RA2026

Similar submodules of projective modules

Alborz Azarang

We introduce a similarity relation between submodules of a module $M$ over a ring $R$ , extending the classical notion of similarity for right ideals. Focusing on (faithfully) proje…

math.RA2026

Non-commutative rings with infinitely many maximal subrings

Alborz Azarang

We study rings with infinitely (only finitely) many maximal subrings. We prove that if $M$ is a maximal left/right ideal of a ring $T$ which is not an ideal of $T$ , and $R$ is the…

math.RA2024

Maximal subrings of certain non-commutative rings

Alborz Azarang

The existence of maximal subrings in certain non-commutative rings, especially in rings which are integral over their centers, are investigated. We prove that if a ring $T$ is inte…

math.RA2024

Maximal subrings of division rings

Alborz Azarang

The structure and the existence of maximal subrings in division rings are investigated. We see that if $R$ is a maximal subring of a division ring $D$ with center $F$ and $N(R)\neq…

math.RA2024

Classical ideals theory of maximal subrings in non-commutative rings

Alborz Azarang

Let $R$ be a maximal subring of a ring $T$ . In this paper we study relation between some important ideals in the ring extension $R \subseteq T$ . In fact, we would like to find some…

math.RA2024

The conductor ideals of maximal subrings in non-commutative rings

Alborz Azarang

Let $R$ be a maximal subring of a ring $T$ , and $(R : T)$ , $(R : T)_{l}$ and $(R : T)_{r}$ denote the greatest ideal, left ideal and right ideal of $T$ which are contained in $R$ , respective…

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.…

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…