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

Source abstract

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