Certain Semigroup With Decomposition And Its Promotion

This paper mainly deals with strong bands or bands of some semigroups and presents their structures. Also this paper offers the structure of normal band semirings.First, we define the pseudo梤ight quasi normal band, at the basic of the defination of the strong band, we get the structure of the pseudo? right quasi normal band. That is it ,A pseudo梤ight quasi normal band can be seen as the strong right quasi normal band of left groups.Furtherly, we show the structure of the orthodox pseudo梤ight quasi normal band of groups and the normal band of left梐rchimedean semigroups. Example, A quasi medial and weakly separative semigroup is a normal band of commutative cancerlative semigroups and furtherly it can be imbeded into a strong semilattice of rectangular Albel groups.At last, we proof that a semigroup is a semilattice of cancellative .ff梘roups if and only if it is .憈梤egular and separable; a band semiring is a normal band semiring if and only if it is a spined product of a left梟ormal band semiring and a right梟ormal band semiring.