On Several Types Of Semi-ring Structure And Decomposition

Several classes of semirings are studied in this paper. The main results are as following:1. The class of orthodox semirings and the class of rectangular semirings are introduced and studied; then a sufficient and necessary condition that a semiring is a distributive lattice of rectangular semirings is given; particularly, for a distributive of rectangular semirings S, we have that S is a sturdy distributive of a rectangular semirings if and only if the additive semigroup of S is a sturdy semilattice.2. The class of N-orthodox semirings and the class of N-rectangular semir-ings are introduced and studied; it is also proved that the N-orthodox semir-ings is a b-lattice of N-rectangular semirings; then additive semigroup of N-rectangular semirings is a rectangular group and each the class of H+ is a S-semilattice are showed.3. Particularly, for a b-lattice of a N-rectangular semirings S, we show that S is a sturdy b-lattice of a N-rectangular semirings if and only if the additive semigroup of S is a sturdy semilattice.