Geodesic
S-Zariski topology on s-spectrum of modules
Filomat, Tome 36 (2022) no. 20, p. 7103

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DOI

Let R be a commutative ring with nonzero identity and M be an R-module. In this paper, first we give some relations between S-prime and S-maximal submodules that are generalizations of prime and maximal submodules, respectively. Then we construct a topology on the set of all S-prime submodules of M , which is generalization of prime spectrum of M. We investigate when Spec S (M) is T 0 and T 1-space. We also study on some continuous maps and irreducibility on Spec S (M). Moreover, we introduce the notion of S-radical of a submodule N of M and use it to show the irreducibility of S-variety V S (N).
DOI : 10.2298/FIL2220103Y
Classification : 13A15, 13C13, 54B35
Keywords: Zariski topology, prime spectrum, S-prime spectrum, S-maximal ideal 
Eda Yildiz; Bayram Ali Ersoy; Ünsal Tekir. S-Zariski topology on s-spectrum of modules. Filomat, Tome 36 (2022) no. 20, p. 7103 . doi: 10.2298/FIL2220103Y
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     title = {S-Zariski topology on s-spectrum of modules},
     journal = {Filomat},
     pages = {7103 },
     year = {2022},
     volume = {36},
     number = {20},
     doi = {10.2298/FIL2220103Y},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2220103Y/}
}
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