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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Pseudoprime $ l$-ideals in a class of $ f$-rings


Author: Suzanne Larson
Journal: Proc. Amer. Math. Soc. 104 (1988), 685-692
MSC: Primary 06F25; Secondary 16A12
MathSciNet review: 964843
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Abstract: In a commutative $ f$-ring, an $ l$-ideal $ I$ is called pseudoprime if $ ab = 0$ implies $ a \in I$ or $ b \in I$, and is called square dominated if for every $ a \in I,\vert a\vert \leq {x^2}$ for some $ x \in A$ such that $ {x^2} \in I$. Several characterizations of pseudoprime $ l$-ideals are given in the class of commutative semiprime $ f$-rings in which minimal prime $ l$-ideals are square dominated. It is shown that the hypothesis imposed on the $ f$-rings, that minimal prime $ l$-ideals are square dominated, cannot be omitted or generalized.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0964843-2
PII: S 0002-9939(1988)0964843-2
Article copyright: © Copyright 1988 American Mathematical Society