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Structure of Semigroups

Published online by Cambridge University Press:  20 November 2018

Hans-Jürgen Hoehnke
Hans-Jürgen Hoehnke*
Affiliation:
Deutsche Akademie der Wis sens chaften zu Berlin, Forschungsgemeinschaft, Institut für Reine Mathematik
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The treatment of semigroups given in a previous paper (3) is based upon representations of a semigroup by means of transformations of a set (cf. also 12). In this paper we try to remove the assumption of the existence of a zero element proposed in (3). In accordance with our general programme explained at the beginning of (3) we utilize certain minimum conditions in order to gain more information on the structure of semigroups.

Our main results are structure theorems on primitive semigroups which have irreducible right ideals generated by idempotents (§§15-17). As we have shown in (5), these theorems permit the explicit construction of primitive semigroups.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 449 - 491
Copyright
Copyright © Canadian Mathematical Society 1966

References

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