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arXiv · 1812.02456

Quasi-prime ideals

Abolfazl Tarizadeh·Mohsen Aghajani
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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.

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Abolfazl Tarizadeh, Mohsen Aghajani. 2018-12-06. Quasi-prime ideals. https://arxiv.org/abs/1812.02456

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