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## Persian Tar and Tonbak in Dastgah e Chahargah

1 Apr

This is the full concert of my brother, Parham and I in Persian mode, Dastgah-e-Chahargah, in Tehran, Iran

http://www.parhamnassehpoor.com

## Peyman Nasehpour at Mathematics Genealogy Project Website

1 Apr

The mission of Mathematics Genealogy Project is to compile information about all the mathematicians of the world. They earnestly solicit information from all schools who participate in the development of research level mathematics and from all individuals who may know desired information.

Recently they listed me here: http://www.genealogy.ams.org/id.php?id=151682

Also when I was searching the page of the late Mohsen Hachtroudi, surprisingly I didn’t find it and by searching in different resources, I gathered the information and submitted to Math. Genea. Proj. Website and now he has a page:

http://www.genealogy.ams.org/id.php?id=24177

I have also noticed that Gholamhossein Mossaheb is not listed there, but up to now I have not found a good resource to submit it.

## Shajarian to congratulate Persian new year

20 Mar

Maestro Mohammad Reza Shajarian congratulate Nowruz (Persian new year).

18 Mar

Happy Nowruz

## In remembrance of professor Mohsen Hachtroudi

10 Mar

When I was student of professor Abdollah Anwar for learning philosophy and logic, time to time he was mentioning the late professor Mohsen Hachtroudi and his knowledge in different branches of science and art. Yesterday I decided to search in Internet and to find some information about him. First I found the title of his thesis who had written under the
supervision of the very famous French mathematician, Élie Joseph Cartan.

The first point that I noticed was that he had romanized his name as Mohsen Hachtroudi in his Ph.D. thesis. I searched the title of his thesis and finally noticed that some mathematicians have referred his thesis in their works. One of those mathematicians that mentions professor Hachtrouri’s thesis in his works for several times is Joel Merker.

What seemed to me more interesting is that the name of Hachtroudi appears in the title of Merker’s recent work:

Vanishing Hachtroudi curvature and local equivalence to the Heisenberg sphere

The biography of professor Mohsen Hachtroudi at wikipedia

Here is a blog devoted to professor Hachtroudi:

Mohsen Hashtroudi

Professor Hachtroudi’s Ph.D. thesis under the supervision of Elie Cartan:

Hachtroudi, M.: Les espaces d’éléments à connexion projective normale,
Actualités Scientifiques et. Industrielles, vol. 565, Paris, Hermann,
1937. (Info from Joel Merker’s works)

Related keywords: Hachtrudi, Hachtroodi, Hashtrudi, Hashtroudi, Hashtroodi

## Mousavi and Karrubi under House Arrest

20 Feb

Iranian opposition leaders Mir-Hossein Mousavi, his wife Zahra Rahnavard and Mehdi Karroubi have been put under house arrest after protest call on Feb. 14, 2011.

Mir Hossein Mousavi and Zahra Rahnavard under House Arrest

Mehdi Karroubi under House Arrest

## My PhD Thesis is now online at the website of the University of Osnabrück

18 Feb

My PhD thesis with the title “Content Algebras and Zero-Divisors” is now online at the website of the University of Osnabrück:

Institutionelles repOSitorium der Universität Osnabrück: Content Algebras and Zero-Divisors

Abstract: This thesis concerns two topics. The first topic, that is related to the Dedekind-Mertens Lemma, the notion of the so-called content algebra, is discussed in chapter 2. Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module and $c$ the function from $M$ to the ideals of $R$ defined by $c(x) = \cap \lbrace I \colon I \text{~is an ideal of~} R \text{~and~} x \in IM \rbrace$. $M$ is said to be a \textit{content} $R$-module if $x \in c(x)M$, for all $x \in M$. The $R$-algebra $B$ is called a \textit{content} $R$-algebra, if it is a faithfully flat and content $R$-module and it satisfies the Dedekind-Mertens content formula. In chapter 2, it is proved that in content extensions, minimal primes extend to minimal primes, and zero-divisors of a content algebra over a ring which has Property (A) or whose set of zero-divisors is a finite union of prime ideals are discussed. The preservation of diameter of zero-divisor graph under content extensions is also examined. Gaussian and Armendariz algebras and localization of content algebras at the multiplicatively closed set $S^ \prime = \lbrace f \in B \colon c(f) = R \rbrace$ are considered as well.

In chapter 3, the second topic of the thesis, that is about the grade of the zero-divisor modules, is discussed. Let $R$ be a commutative ring, $I$ a finitely generated ideal of $R$, and $M$ a zero-divisor $R$-module. It is shown that the $M$-grade of $I$ defined by the Koszul complex is consistent with the definition of $M$-grade of $I$ defined by the length of maximal $M$-sequences in $I$.

Chapter 1 is a preliminarily chapter and dedicated to the introduction of content modules and also locally Nakayama modules.

Supervisor: Prof. Dr. Winfried Bruns

Important keywords and phrases: modules, commutative rings and algebras, content module, content algebra, weak content algebra, very few zero-divisor, zero-divisor graph, Gaussian algebra, Armendariz algebra, minimal prime ideal, property (A), Gauss’ lemma, Dedekind-Mertens lemma, ZD-module, grade, local cohomology module, homological dimension, McCoy’s property, semigroup ring, semigroup module, locally Nakayama module.

Alternative page for my PhD Thesis:

Content Algebras and Zero-Divisors