Sums of semiprime, 𝑧, and 𝑑𝑙-ideals in a class of 𝑓-rings

Larson, Suzanne

doi:10.1090/S0002-9939-1990-1015682-7

Sums of semiprime, $z,$ and $d\ l$-ideals in a class of $f$-rings
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Proc. Amer. Math. Soc. 109 (1990), 895-901 Request permission

Abstract:

In this paper it is shown that there is a large class of $f$-rings in which the sum of any two semiprime $l$-ideals is semiprime. This result is used to give a class of commutative $f$-rings with identity element in which the sum of any two $z$-ideals which are $l$-ideals is a $z$-ideal and the sum of any two $d$-ideals is a $d$-ideal.

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