On The Properties And Structures Of Several Classes Of Semirings

Algebraic theory of semirings is an active field of Algebra. In this dissertation, we mainly studied the structures of semirings. It obtained the following results:1.We gave the definition and properties of semirings belonging to MRG(?)_l; proved that (?) is a semiring congruence by using the theory of the sturdy frame of type (2,2) type algebras, obtained the subdirect product decomposition of semirings in MRG(?)_l.2.We studied the characterazation and structure of multiplicative Clifford semirings and proved that (?) is the least distributive lattice congruence, obtained the subdirect products decomposition of multiplicative Clifford semirings.3.We studied the rectangular divided semirings and distributive lattice of rectangular divided semirings. We discussed the relation ship between these semirings and their multiplication reduct. Further, we obtained the subdirect products decanposition of them and discussed the distributive lattice of orthodox rectangular divided semirings4. We discussed the properties of idempotent semiring and distributive lattice, and study their difference and sameness, obtained the conditions which idempotent semiring is a distributive lattice.