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(1)Introduction - In the work (l) a generaI disjoint decomposition of semigroups was given, wich can be applied far the case of regular semigroups

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(1)

Introduction - In the work (l) a generaI disjoint decomposition of semigroups was given, wich can be applied far the case of regular

semigroups. The aim of the present paper is to obtain a characteristic decomposition of regular semigroups based on the decomposition studied

in (l). We shall investigate the components of this decomposition and the interrelations between them.

By making use of the work (2) we study the cases of regular semigroups with or without left or right identity elemento

Finally we make some special remarks.

Notations : Far two.sets A, B we write AC.B ii A lS• a

proper subset of B. By magnifying element we mean a left magnifying e lement.

§ 1.

Let S be a semigroup without nonzero annihilator. This is not a proper restriction because every semigroup can be reduced to this

case.

Then S has the following disjoint decomposition:

/1/

5

S - V S. ,

• l

1=0

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