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Equivalent Conditions for a Ring to Be a Multiplication Ring

Published online by Cambridge University Press:  20 November 2018

Joe Leonard Mott
Joe Leonard Mott*
Affiliation:
Louisiana State University Baton Rouge, Louisiana
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In this paper a ring will always mean a commutative ring with identity element. Furthermore, a ring R is called a multiplication ring if, whenever A and B are ideals of R and A is contained in B, there is an ideal C such that A = BC. Noetherian multiplication rings have been studied by Asano (1), Krull (4, 5), and Mori (6, 7). Krull also studied non-Noetherian multiplication rings (3). In (8, 9), Mori studied non-Noetherian multiplication rings which did not necessarily contain an identity element.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 429 - 434
Copyright
Copyright © Canadian Mathematical Society 1964

References

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