Geodesic
Rings in which all Subrings are Ideals. I
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 862-871

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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. 
Kruse, Robert L. Rings in which all Subrings are Ideals. I. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 862-871. doi: 10.4153/CJM-1968-083-1
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[1] 1. Freĭdman, P. A., Rings with idealize/ condition. II, Ucen. Zap. Ural'sk. Gos. Univ. 2 (1959), 35–48. (Russian) Google Scholar

[2] 2. Jones, A. and J. J. Schâffer, Concerning the structure of certain rings, Bol. Fac. Ingen. Agriment. 6 (1957-58), 327–335. Google Scholar

[3] 3. Liu, Shao-Xue, On algebras in which every subalgebra is an ideal, Acta Math. Sinica 14- (1964), 532-537 (Chinese); translated as Chinese Math.-Acta 5 (1964), 571–577. Google Scholar

[4] 4. Rédei, L., Vollidealringe im weiteren Sinn. I, Acta Math. Acad. Sci. Hungar. 3 (1952), 243–268. Google Scholar

[5] 5. Šperling, M., On rings, every subring of which is an ideal, Mat. Sb. 17 (59) (1945), 371–384. Russian) Google Scholar

[6] 6. Szász, F., Die Ringe, deren endlich erzeugbare echte Unterringe Hauptrechtsideale sind, Acta Math. Acad. Sci. Hungar. 13 (1962), 115–132. Google Scholar

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