JP Journal of Algebra, Number Theory and Applications
Volume 2, Issue 2, Pages 181 - 193
(August 2002)
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PRINCIPAL IDEALS AND ASSOCIATE RINGS
Dennis Spellman (USA), Georgia M. Benkart (USA), Anthony M. Gaglione (USA), W. David Joyner (USA), Mark E. Kidwell(USA), Mark D. Meyerson (USA) and William P. Wardlaw (USA)
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Abstract: A commutative ring A with
1 is associate provided whenever two elements
a and b generate the same principal
ideal there is a unit u such that ua = b.
The main results proved here are:
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Every commutative
Noetherian ring with 1 is a subdirect product of
rings which have the property that all their
unital subrings are associate.
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Every commutative ring
embeds into an associate ring.
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Every commutative unital
algebraically closed or principal ideal ring is
associate.
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The direct product of
associate rings is associate. |
Keywords and phrases: associate rings,
principal ideals, model theory. |
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