Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-24T09:34:06.179Z Has data issue: false hasContentIssue false
  • English
  • Français

Rings With Comparability

Published online by Cambridge University Press:  20 November 2018

Miguel Ferrero  and
Alveri Sant’Ana
Miguel Ferrero
Affiliation:
Instituto de Matemática Universidade Federal do Rio Grande do Sul 91509-900, Porto Alegre, Brazil, email: [email protected]
Alveri Sant’Ana
Affiliation:
Instituto de Matemática Universidade Federal do Rio Grande do Sul 91509-900, Porto Alegre, Brazil, email: [email protected]
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 class of rings studied in this paper properly contains the class of right distributive rings which have at least one completely prime ideal in the Jacobson radical. Amongst other results we study prime and semiprime ideals, right noetherian rings with comparability and prove a structure theorem for rings with comparability. Several examples are also given.

Keywords

16U9916P4016D1516N60
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 42 , Issue 2 , 01 June 1999 , pp. 174 - 183
Copyright
Copyright © Canadian Mathematical Society 1999

References

[1] Ara, P., O’Meara, K. C. and Tyukavkin, D. V., Cancellation of projective modules over regular rings with comparability. J. Pure Appl. Algebra 107 (1996), 19–38.Google Scholar
[2] Bessenrodt, C., Brungs, H. H. and Törner, G., Right chain rings, Part 1. Schriftenreihe des Fachbereichs Math. 181, Duisburg Univ., 1990.Google Scholar
[3] Brungs, H. H., Rings with a distributive lattice of right ideals. J. Algebra 40 (1976), 392–400.Google Scholar
[4] Ferrero, M. and Törner, G., Rings with annihilator chain condition and right distributive rings. Proc. Amer. Math. Soc. 119 (1993), 401–405.Google Scholar
[5] Ferrero, M. and Törner, G., On the ideal structure of right distributive rings. Comm. Algebra (8) 21 (1993), 2697–2713.Google Scholar
[6] Ferrero, M. and Törner, G., On waists of right distributive rings. ForumMath. 7 (1995), 419–433.Google Scholar
[7] Mazurek, R., Distributive rings with Goldie dimension one. Comm. Algebra (3) 19 (1991), 931–944.Google Scholar
[8] Mazurek, R. and Puczyłowski, E., On nilpotent elements of distributive rings. Comm. Algebra (2) 18 (1990), 463–471.Google Scholar
[9] Sant’Ana, A., Anéis e Mòdulos com comparabilidade. Ph. D. thesis, Unicamp, Brazil, 1995.Google Scholar
[10] Stephenson, W.,Modules whose lattice of submodules is distributive. Proc. London Math. Soc. 28 (1974), 291–310.Google Scholar