Cyclic left and torsion-theoretic spectra of modules and their relations
Algebra and discrete mathematics, Tome 20 (2015) no. 2, pp. 286-296.

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

In this paper, strongly-prime submodules of a cyclic module are considered and their main properties are given. On this basis, a concept of a cyclic spectrum of a module is introduced. This spectrum is a generalization of the Rosenberg spectrum of a noncommutative ring. In addition, some natural properties of this spectrum are investigated, in particular, its functoriality is proved.
Keywords: strongly-prime ideal, strongly-prime module, cyclic spectrum, torsion-theoretic spectrum, localizations.
@article{ADM_2015_20_2_a6,
     author = {Marta Maloid-Glebova},
     title = {Cyclic left and torsion-theoretic spectra of modules and their relations},
     journal = {Algebra and discrete mathematics},
     pages = {286--296},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2015_20_2_a6/}
}
TY  - JOUR
AU  - Marta Maloid-Glebova
TI  - Cyclic left and torsion-theoretic spectra of modules and their relations
JO  - Algebra and discrete mathematics
PY  - 2015
SP  - 286
EP  - 296
VL  - 20
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2015_20_2_a6/
LA  - en
ID  - ADM_2015_20_2_a6
ER  - 
%0 Journal Article
%A Marta Maloid-Glebova
%T Cyclic left and torsion-theoretic spectra of modules and their relations
%J Algebra and discrete mathematics
%D 2015
%P 286-296
%V 20
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2015_20_2_a6/
%G en
%F ADM_2015_20_2_a6
Marta Maloid-Glebova. Cyclic left and torsion-theoretic spectra of modules and their relations. Algebra and discrete mathematics, Tome 20 (2015) no. 2, pp. 286-296. http://geodesic.mathdoc.fr/item/ADM_2015_20_2_a6/

[1] Beachy J. A., “Some aspects of noncommutative localization”, Noncommutative Ring Theory, LNM, 545, Spriger-Verlag, Berlin, 1975, 2–31 | MR

[2] Kaučikas A., “On the left strongly prime modules and their radicals”, Lietuvos matematikos rinkinys, LMD darbai, 51, 2010, 31–34

[3] Dauns J., “Prime modules”, Reine Angew. Math., 298 (1978), 156–181 | MR | Zbl

[4] Gabriel P., “Des Categories Abeliennes”, Bull. Soc. Math. France, 90 (1962), 323–448 | MR | Zbl

[5] Golan J. S., “Topologies on the Torsion-Theoretic Spectrum of a Noncommutatie Ring”, Pacific Journal of Mathematics, 51:2 (1974), 439–450 | DOI | MR | Zbl

[6] Jara P., Verhaeghe P., Verschoren A., “On the left spectrum of a ring”, Communs. Algebra, 22:8 (1994), 2983–3002 | DOI | MR | Zbl

[7] Letzter E. S., “On continuous and adjoint morphisms between non-commutative prime spectra”, Proc. Edinbourgh Math. Soc., 49 (2006), 367–381 | DOI | MR | Zbl

[8] Rosenberg A. L., “The left spectrum, the Levitski radical, and noncommutative schemes”, Proc. Nat. Acad. Sci. USA, 1990, no. 87, 8583–8586 | DOI | MR | Zbl

[9] Reyes M. L., “Obstructing extensions of the functors Spec to noncommutative rings”, Israel J. Math., 192 (2012), 667–698 | DOI | MR | Zbl