The lattice of pre-natural classes of modules

Authors
Citation
Yq. Zhou, The lattice of pre-natural classes of modules, J PURE APPL, 140(2), 1999, pp. 191-207
Citations number
22
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF PURE AND APPLIED ALGEBRA
ISSN journal
00224049 → ACNP
Volume
140
Issue
2
Year of publication
1999
Pages
191 - 207
Database
ISI
SICI code
0022-4049(19990728)140:2<191:TLOPCO>2.0.ZU;2-6
Abstract
In this paper, we introduce and study a new complete lattice whose elements are the so-called pre-natural classes of R-modules. This lattice contains a complete sublattice isomorphic to the complete lattice of all linear topo logies of R and a sublattice anti-isomorphic to the frame of all hereditary torsion theories of R. Moreover, the complete Boolean lattice of all natur al classes of R-modules is a sublattice of this lattice. Various properties of this new lattice are formulated and some applications to the ring R are given. (C) 1999 Elsevier Science B.V. All rights reserved.