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	Volume 2, Issue 3 Pg 205 - 315 (December 2002)
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Volume 1 (2001)

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JP Journal of Algebra, Number Theory and Applications

JP Journal of Algebra, Number Theory and Applications
Volume 2, Issue 2, Pages 181 - 193 (August 2002)

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)

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:

Every commutative Noetherian ring with 1 is a subdirect product of rings which have the property that all their unital subrings are associate.
Every commutative ring embeds into an associate ring.
Every commutative unital algebraically closed or principal ideal ring is associate.
The direct product of associate rings is associate.

Keywords and phrases: associate rings, principal ideals, model theory.

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