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A nil-extension of a completely simple semigroup. (English) Zbl 0567.20041
The authors prove that if S is a semigroup, then (i) S is power-regular if and only if S is a nil-extension of a completely simple semigroup, (ii) S is a nil-extension of a left group if and only if S is power- regular and the set of all idempotents of S is a left zero band, (iii) S is a power group if and only if S is a nil-extension of a group, (iv) S is a nil-extension of a rectangular band if and only if (\(\forall a,b\in S)\) (\(\exists m\in N)\) \((a^ m=a^ mba^ m)\).
Reviewer: Ph.Das

MSC:
20M10 General structure theory for semigroups
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