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Rings in which all Subrings are Ideals. I

Published online by Cambridge University Press:  20 November 2018

Robert L. Kruse
Robert L. Kruse*
Affiliation:
Sandia Laboratory, Albuquerque, N.M.
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In analogy with Hamiltonian groups, an associative ring in which every subring is a two-sided ideal is called a Hamiltonian ring, or, more concisely, an H-ring. Several attempts at classification of H-rings have been made. H-rings generated by a single element have been studied by M. Šperling (5), L. Rédei (4), and A. Jones and J. J. Schäffer (2). H-rings enjoying additional properties have been characterized by F. Szász (e.g., 6), and by S.-X. Liu (3). A class of closely related rings has been studied by P. A. Freĭdman (1). In the present paper and its sequel all H-rings are classified and completely described in terms of their generators and relations.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 862 - 871
Copyright
Copyright © Canadian Mathematical Society 1968

References

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