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Francisco E. Alarcón ... et al KYUNGPOOK UNIVERSITY 2000 Kyungpook mathematical journal Vol.40 No.2
We characterize semirings where every ideal is prime (fully prime semirings) as those having a totally ordered lattice with every ideal idempotents. We provide a characterizaton, in terms of the values of n and i, for the finite semirings B(n, i) that are fully prime. We also provide a characterization of the subtractive ideals in the semirings B(n, i).