MODULES AND THE SECOND CLASSICAL ZARISKI TOPOLOGY
Küçük Resim Yok
Tarih
2018
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Univ Studi Catania, Dipt Matematica
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
Let R be an associative ring with identity and Spec(s)(M) denote the set of all second submodules of a right R-module M. In this paper, we present a number of new results for the second classical Zariski topology on Spec(s)(M) for a right R-module M. We obtain a characterization of semisimple modules by using the second spectrum of a module. We prove that if R is a ring such that every right primitive factor of R is right artinian, then every non-zero submodule of a second right R-module M is second if and only if M is a fully prime module. We give some equivalent conditions for Spec(s)(M) to be a Hausdorff space or T-i-space when the right R-module M has certain algebraic properties. We obtain characterizations of commutative Quasi-Frobenius and artinian rings by using topological properties of the second classical Zariski topology. We give a full characterization of the irreducible components of Spec(s)(M) for a non-zero injective right module M over a ring R such that every prime factor of R is right or left Goldie.
Açıklama
Anahtar Kelimeler
Second Submodule, Second Spectrum, Prime Submodule, Second Classical Zariski Topology, Noncommutative Rings, Prime Spectrum, Dual Notion, Submodules
Kaynak
Matematiche
WoS Q Değeri
N/A
Scopus Q Değeri
Q3
Cilt
73
Sayı
1
