Hostname: page-component-5cf477f64f-h6p2m Total loading time: 0 Render date: 2025-04-06T13:04:48.589Z Has data issue: false hasContentIssue false
  • English
  • Français

THE CLASSIFICATION OF COMMUTATIVE TORSION FILIAL RINGS

Part of: Theory of modules and ideals Ring extensions and related topics Modules, bimodules and ideals

Published online by Cambridge University Press:  18 July 2013

R. R. ANDRUSZKIEWICZ  and
K. PRYSZCZEPKO
R. R. ANDRUSZKIEWICZ
Affiliation:
Institute of Mathematics, University of Białystok, 15-267 Białystok, Akademicka 2, Poland email randrusz@math.uwb.edu.pl
K. PRYSZCZEPKO*
Affiliation:
Institute of Mathematics, University of Białystok, 15-267 Białystok, Akademicka 2, Poland email randrusz@math.uwb.edu.pl
*
✉karolp@math.uwb.edu.pl
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The aim of this paper is to give a classification theorem for commutative torsion filial rings.

Keywords

idealfilial ring

MSC classification

Secondary: 16D25: Ideals 13C05: Structure, classification theorems 13B02: Extension theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 95 , Issue 3 , December 2013 , pp. 289 - 296
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

References

Andrijanov, V. I., ‘Mixed Hamiltonian nilrings’, Ural. Gos. Univ. Mat. Zap. 5 (3) (1966), 15–30(in Russian).Google Scholar
Andrijanov, V. I., ‘Periodic Hamiltonian rings’, Mat. Sb. (N.S.) 74 (116) (1967), 241–261; translation in Mat. Sb. 74(116) (1967), 225–241.Google Scholar
Andruszkiewicz, R. R., ‘The classification of integral domains in which the relation of being an ideal is transitive’, Comm. Algebra. 31 (2003), 2067–2093.CrossRefGoogle Scholar
Andruszkiewicz, R. R. and Pryszczepko, K., ‘A classification of commutative reduced filial rings’, Comm. Algebra. 37 (2009), 3820–3826.CrossRefGoogle Scholar
Andruszkiewicz, R. R. and Pryszczepko, K., ‘The classification of commutative noetherian, filial rings with identity’, Comm. Algebra. 40 (2012), 1690–1703.CrossRefGoogle Scholar
Andruszkiewicz, R. R. and Puczyłowski, E. R., ‘On filial rings’, Port. Math. 45 (1988), 139–149.Google Scholar
Filipowicz, M. and Puczyłowski, E. R., ‘Left filial rings’, Algebra Colloq. 11 (3) (2004), 335–344.Google Scholar
Filipowicz, M. and Puczyłowski, E. R., ‘The structure of left filial algebras over a field’, Taiwanese J. Math. 13 (3) (2009), 1017–1029.CrossRefGoogle Scholar
Kruse, R. L., ‘Rings with periodic additive group in which all subrings are ideals’, Dissertation, California Institute of Technology, 1964.Google Scholar
Kruse, R. L., ‘Rings in which all subrings are ideals’, Canad. J. Math. 20 (1968), 862–871.CrossRefGoogle Scholar
Redei, L., ‘Vollidealringe im weiteren Sinn. I’, Acta Math. Acad. Sci. Hungar. 3 (1952), 243–268.CrossRefGoogle Scholar
Redei, L., ‘Die Vollidealringe’, Monatsh. Math. 56 (1952), 89–95.CrossRefGoogle Scholar