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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Ternary rings

Author: W. G. Lister
Journal: Trans. Amer. Math. Soc. 154 (1971), 37-55
MSC: Primary 16.96
MathSciNet review: 0272835
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Abstract: We characterize those additive subgroups of rings which are closed under the triple ring product, then discuss their imbeddings in rings, their representation in terms of two types of modules, a radical theory, the structure of those which satisfy a minimum condition for certain ideals, and finally the classification of those which are simple ternary algebras over an algebraically closed or real closed field.

References [Enhancements On Off] (What's this?)

  • [1] N. Jacobson, Structure of rings, Amer. Math. Soc. Colloq. Publ., vol. 37, Amer. Math. Soc., Providence, R. I., 1956. MR 18, 373. MR 0081264 (18:373d)
  • [2] W. G. Lister, A structure theory of Lie triple systems, Trans. Amer. Math. Soc. 72 (1952), 217-242. MR 13, 619. MR 0045702 (13:619d)
  • [3] -, On variants of Lie triple systems and their Lie algebras, Kumamato J. Sci. Ser. A 7 (1965/67), 73-83. MR 37 #6335. MR 0230775 (37:6335)
  • [4] M. F. Smiley, An introduction to Hestenes ternary rings, Amer. Math. Monthly 76 (1969), 245-248. MR 39 #1484. MR 0240130 (39:1484)

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Keywords: Imbedding, enveloping ring, ternary module, radical, minimum condition, simplicity
Article copyright: © Copyright 1971 American Mathematical Society

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