3 citations · 9 across the 30 of their papers we have counts for
38 papers
A counterexample to a question on the maximality of purely-primes
Abolfazl Tarizadeh
By using an advanced model of AI, it is proved that there exists a commutative ring having a purely-prime ideal which is not purely-maximal. This gives a counterexample to \cite[Co…
Ideal class group of an extension of rings and Picard group
Abolfazl Tarizadeh
For any extension of commutative rings , by using invertible ideals, we first define an Abelian group $\Cl(A,B)$, that we call the ideal class group of this extension…
Splitting in a complete local ring and decomposition its group of units
Abolfazl Tarizadeh
Let be a complete local ring (not necessarily Noetherian). As the first main result of this article, we prove that in the unequal characteristic case $\Char(R)\neq\Char(k…
Cardinality of groups and rings via the idempotency of infinite cardinals
Abolfazl Tarizadeh
An important classical result in ZFC asserts that every infinite cardinal number is idempotent. Using this fact, we obtain several algebraic results in this article. The first resu…
Connected components of qcqs schemes and projective spaces
Abolfazl Tarizadeh
In this article, we first prove a general result in topology which states that every quasi-component of a quasi-spectral space is connected. \\ As an application, the structure of…
Spectral closures of an infinite subset of the prime spectrum
Abolfazl Tarizadeh
In the literature, there is no known general method (formula) to compute the Zariski closure of an ``infinite'' subset of the prime spectrum. This problem indeed deals with the pri…