Quasi-prime ideals
Commutative Algebra
2018-12-07 v1
Abstract
In this paper, the new concept of quasi-prime ideal is introduced which at the same time generalizes the `prime ideal' and `primary ideal' notions. Then a natural topology on the set of quasi-prime ideals of a ring is introduced which generalizes the Zariski topology. The basic properties of the quasi-prime spectrum are studied and several interesting results are obtained. Specially, it is proved that if the Grothendieck t-functor is applied on the quasi-prime spectrum then the prime spectrum is deduced. It is also shown that there are the cases that the prime spectrum and quasi-prime spectrum do not behave similarly.
Cite
@article{arxiv.1812.02456,
title = {Quasi-prime ideals},
author = {Abolfazl Tarizadeh and Mohsen Aghajani},
journal= {arXiv preprint arXiv:1812.02456},
year = {2018}
}
Comments
9 pages