Semirings of cyclic types

The authors investigate semirings of cyclic types from the algebraic point of view. To simplify and facilitate the analysis, the local Fourier transform of these semirings is introduced. The authors describe zero divisors, nilpotent elements, invertible elements, idempotents, and the Jacobson radical. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 2, pp. 175–192, 2006.