The q.Zariski topology on the quasi-primary spectrum of a ring
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2021), pp. 3-10.

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $R$ be a commutative ring with identity. We topologize $\mathrm{q.Spec}(R)$, the quasi-primary spectrum of $R$, in a way similar to that of defining the Zariski topology on the prime spectrum of $R$, and investigate the properties of this topological space. Rings whose q.Zariski topology is respectively $T_0$, $T_1$, irreducible or Noetherian are studied, and several characterizations of such rings are given.
@article{BASM_2021_3_a0,
     author = {Mahdi Samiei and Hosein Fazaeli Moghimi},
     title = {The {q.Zariski} topology on the quasi-primary spectrum of a ring},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {3--10},
     publisher = {mathdoc},
     number = {3},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2021_3_a0/}
}
TY  - JOUR
AU  - Mahdi Samiei
AU  - Hosein Fazaeli Moghimi
TI  - The q.Zariski topology on the quasi-primary spectrum of a ring
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2021
SP  - 3
EP  - 10
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BASM_2021_3_a0/
LA  - en
ID  - BASM_2021_3_a0
ER  - 
%0 Journal Article
%A Mahdi Samiei
%A Hosein Fazaeli Moghimi
%T The q.Zariski topology on the quasi-primary spectrum of a ring
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2021
%P 3-10
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BASM_2021_3_a0/
%G en
%F BASM_2021_3_a0
Mahdi Samiei; Hosein Fazaeli Moghimi. The q.Zariski topology on the quasi-primary spectrum of a ring. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2021), pp. 3-10. http://geodesic.mathdoc.fr/item/BASM_2021_3_a0/

[1] Atiyah M. F., McDonald I. G., Introduction to commutative algebra, Addison Weisley Publishing Company, Inc, 1969 | MR | Zbl

[2] Azizi A., “Strongly irreducible ideals”, J. Aust. Math. Soc., 84 (2008), 145–154 | DOI | MR | Zbl

[3] Fuchs L., “On quasi-primary ideals”, Acta Sci. Math. (Szeged), 11 (1947), 174–183 | MR | Zbl

[4] Matsumura H., Commutative ring theory, Cambridge University Press, Cambridge, 1992 | MR

[5] Zhang G., Tong W., Wang F., “Gelfand factor rings and weak Zariski topologies”, Comm. Algebra, 35:8 (2007), 2628–2645 | DOI | MR | Zbl

[6] Zhang G., Tong W., Wang F., “Spectrum of a noncommutative ring”, Comm. Algebra, 34:8 (2006), 2795–2810 | DOI | MR | Zbl