In this paper it is shown that there is a large class of f-rings in which the sum of any two semiprime i-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 i-ideals is a z-ideal and the sum of any two d-ideals is a d-ideal.
First published in Proceedings of the American Mathematical Society in 1990, published by the American Mathematical Society
Larson, S. Sums of Semiprime, Z, and D L-Ideals in a Class of F-Rings, Proceedings of the American Mathematical Society. vol. 109 (1990) pp. 895-901.