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THE CLASSIFICATION OF COMMUTATIVE TORSION FILIAL RINGS

Published online by Cambridge University Press:  18 July 2013

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
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Abstract

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

Type
Research Article
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

References

Andrijanov, V. I., ‘Mixed Hamiltonian nilrings’, Ural. Gos. Univ. Mat. Zap. 5 (3) (1966), 1530(in Russian).Google Scholar
Andrijanov, V. I., ‘Periodic Hamiltonian rings’, Mat. Sb. (N.S.) 74 (116) (1967), 241261; 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), 20672093.CrossRefGoogle Scholar
Andruszkiewicz, R. R. and Pryszczepko, K., ‘A classification of commutative reduced filial rings’, Comm. Algebra. 37 (2009), 38203826.CrossRefGoogle Scholar
Andruszkiewicz, R. R. and Pryszczepko, K., ‘The classification of commutative noetherian, filial rings with identity’, Comm. Algebra. 40 (2012), 16901703.CrossRefGoogle Scholar
Andruszkiewicz, R. R. and Puczyłowski, E. R., ‘On filial rings’, Port. Math. 45 (1988), 139149.Google Scholar
Filipowicz, M. and Puczyłowski, E. R., ‘Left filial rings’, Algebra Colloq. 11 (3) (2004), 335344.Google Scholar
Filipowicz, M. and Puczyłowski, E. R., ‘The structure of left filial algebras over a field’, Taiwanese J. Math. 13 (3) (2009), 10171029.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), 862871.CrossRefGoogle Scholar
Redei, L., ‘Vollidealringe im weiteren Sinn. I’, Acta Math. Acad. Sci. Hungar. 3 (1952), 243268.CrossRefGoogle Scholar
Redei, L., ‘Die Vollidealringe’, Monatsh. Math. 56 (1952), 8995.CrossRefGoogle Scholar