In this paper we introduce and study the left spectrum and the torsion-theoretic spectrum of modules and establish some connections between them. In particular, the fact that for a multiplication module the left torsion-theoretic spectrum is a quotient space is proved. Also, the notion of locally-prime torsion theory is given, some properties of such torsion theories are presented. Is proved the fact, that symmetric extended (by Belluce) torsion-theoretic spectrum of a ring (module), under certain restrictions, is a spectral space. Also we construct spectrum for the left spectrum of a ring, that, in its turn, is based on the theory of strongly-prime modules. As a technical equipment we use general facts from the torsion theory in the category of left modules over associative rings and some generalizations of technical results from previously published work of many authors.
Real Time Impact Factor:
Pending
Author Name: M. O. Maloid-Glebova
URL: View PDF
Keywords: module spectrum; multiplication module; locally-prime torsion theory; spectral space
ISSN: 1027-4634
EISSN:
EOI/DOI:
Add Citation
Views: 3969