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Proceedings of the American Mathematical Society

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Direct product decomposition of commutative semi-simple rings


Author: Alexander Abian
Journal: Proc. Amer. Math. Soc. 24 (1970), 502-507
MSC: Primary 13.50
DOI: https://doi.org/10.1090/S0002-9939-1970-0258815-X
MathSciNet review: 0258815
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper it is shown that a commutative semisimple ring is isomorphic to a direct product of fields if and only if it is hyperatomic and orthogonally complete.


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

  • [1] Nathan Jacobson, Structure of rings, American Mathematical Society, Colloquium Publications, vol. 37, American Mathematical Society, 190 Hope Street, Prov., R. I., 1956. MR 0081264
  • [2] Garrett Birkhoff, Lattice theory, Third edition. American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. MR 0227053

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0258815-X
Keywords: Decomposition as direct product, commutative semisimple ring, decomposition as complete direct sum, commutative ring, nonzero nilpotent element
Article copyright: © Copyright 1970 American Mathematical Society