Honest submodules

Pascual Jara

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 1, page 225-241
  • ISSN: 0011-4642

Abstract

top
Lattices of submodules of modules and the operators we can define on these lattices are useful tools in the study of rings and modules and their properties. Here we shall consider some submodule operators defined by sets of left ideals. First we focus our attention on the relationship between properties of a set of ideals and properties of a submodule operator it defines. Our second goal will be to apply these results to the study of the structure of certain classes of rings and modules. In particular some applications to the study and the structure theory of torsion modules are provided.

How to cite

top

Jara, Pascual. "Honest submodules." Czechoslovak Mathematical Journal 57.1 (2007): 225-241. <http://eudml.org/doc/31126>.

@article{Jara2007,
abstract = {Lattices of submodules of modules and the operators we can define on these lattices are useful tools in the study of rings and modules and their properties. Here we shall consider some submodule operators defined by sets of left ideals. First we focus our attention on the relationship between properties of a set of ideals and properties of a submodule operator it defines. Our second goal will be to apply these results to the study of the structure of certain classes of rings and modules. In particular some applications to the study and the structure theory of torsion modules are provided.},
author = {Jara, Pascual},
journal = {Czechoslovak Mathematical Journal},
keywords = {closed submodules; honest submodules; topological filters; closed submodules; honest submodules; topological filters; closure operators; lattices of submodules; torsion modules},
language = {eng},
number = {1},
pages = {225-241},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Honest submodules},
url = {http://eudml.org/doc/31126},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Jara, Pascual
TI - Honest submodules
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 1
SP - 225
EP - 241
AB - Lattices of submodules of modules and the operators we can define on these lattices are useful tools in the study of rings and modules and their properties. Here we shall consider some submodule operators defined by sets of left ideals. First we focus our attention on the relationship between properties of a set of ideals and properties of a submodule operator it defines. Our second goal will be to apply these results to the study of the structure of certain classes of rings and modules. In particular some applications to the study and the structure theory of torsion modules are provided.
LA - eng
KW - closed submodules; honest submodules; topological filters; closed submodules; honest submodules; topological filters; closure operators; lattices of submodules; torsion modules
UR - http://eudml.org/doc/31126
ER -

References

top
  1. 10.1007/BF02851268, Rend. Circ. Mat. Palermo, II Ser. 12 (1963), 353–356. (1963) MR0167523DOI10.1007/BF02851268
  2. Lectures on algebraic quantum groups, Advanced Courses in Mathematics—CRM Barcelona, Birkhäuser, Basel, 2002. (2002) MR1898492
  3. 10.1023/A:1008622617846, Applied Categorical Structures 8 (2000), 317–326. (2000) MR1785851DOI10.1023/A:1008622617846
  4. Abelian Groups, Pergamon Press, Oxford, 1967. (1967) MR0111783
  5. Torsion Theories, Pitman Monographs and Surveys in Pure and Appl. Math., No. 29, Longman Sc. & Tech., Essex, 1986. (1986) Zbl0657.16017MR0880019
  6. Ring Theory. Nonsingular Rings and Modules, Monographs and Textbooks in Pure and Applied Mathematics, No. 33, Marcel Dekker, Inc., New York-Basel, 1976. (1976) Zbl0336.16001MR0429962
  7. 10.1090/S0002-9939-1994-1211579-1, Proc. Amer. Math. Soc. 121 (1994), 1017–1025. (1994) MR1211579DOI10.1090/S0002-9939-1994-1211579-1
  8. Superhonesty for modules and Abelian groups, Chinese J. Math. 12 (1984), 87–95. (1984) MR0759798
  9. A note on generalized honest subgroups of Abelian groups, Comment. Math. Univ. St. Paul. 36 (1987), 145–148. (1987) MR0919447

NotesEmbed ?

top

You must be logged in to post comments.