Based on the concept of accessible subhemirings and inspired by the work on the general Kurosh-Amitsur radical theory for rings, this paper studies the lower radical classes and the hereditary radical classes of hemirings. We characterize radical classes of hemirings, and construct a lower radical class from a homomorphically closed class. We provide a necessary and sufficient condition under which an upper radical class of hemirings becomes hereditary and prove that an upper radical class of a regular class of semirings is hereditary. Besides, we show that the Brown-McCoy radical class and a Jacobson-type radical class are hereditary.

Tbilisi Mathematical Journal, Vol. 7(1) (2014), pp. 69-74