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.
- Nathan Jacobson, Structure of rings, American Mathematical Society Colloquium Publications, Vol. 37, American Mathematical Society, 190 Hope Street, Prov., R. I., 1956. MR 0081264
- Garrett Birkhoff, Lattice theory, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. MR 0227053
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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