Pseudoprime 𝑙-ideals in a class of 𝑓-rings

Larson, Suzanne

doi:10.1090/S0002-9939-1988-0964843-2

Pseudoprime $l$-ideals in a class of $f$-rings
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by Suzanne Larson

Proc. Amer. Math. Soc. 104 (1988), 685-692

DOI: https://doi.org/10.1090/S0002-9939-1988-0964843-2

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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 $a \in I,|a| \leq {x^2}$ 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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