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ON COMMUTATIVE REDUCED FILIAL RINGS

Part of: Modules, bimodules and ideals

Published online by Cambridge University Press:  21 October 2009

R. R. ANDRUSZKIEWICZ  and
K. PRYSZCZEPKO
R. R. ANDRUSZKIEWICZ
Affiliation:
Institute of Mathematics, University of Białystok, 15-267 Białystok, Akademicka 2, Poland (email: [email protected])
K. PRYSZCZEPKO*
Affiliation:
Institute of Mathematics, University of Białystok, 15-267 Białystok, Akademicka 2, Poland (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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A ring in which every accessible subring is an ideal is called filial. We continue the study of commutative reduced filial rings started in [R. R. Andruszkiewicz and K. Pryszczepko, ‘A classification of commutative reduced filial rings’, Comm. Algebra to appear]. In particular we describe the Noetherian commutative reduced rings and construct nontrivial examples of commutative reduced filial rings without ideals which are domains.

Keywords

idealfilial ringreduced ringp-adic numbers

MSC classification

Secondary: 16D25: Ideals
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 81 , Issue 2 , April 2010 , pp. 310 - 316
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

References

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