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The Translational Hull of a Semilattice of Weakly Reductive Semigroups

Published online by Cambridge University Press:  20 November 2018

Mario Petrich
Mario Petrich*
Affiliation:
The Pennsylvania State University, University Park, Pennsylvania
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The translational hull is of central importance in the construction of ideal extensions and the study of densely embedded ideals particularly for weakly reductive semigroups (see [4, Chapter III]). The translational hull of semigroups belonging to a few special classes is known in an explicit form, and for some other classes of semigroups, certain properties of their translational hulls have been established (see [4, Chapter V]). We have generalized in [5] the concept of an inverse limit of groups in order to give a construction of the translational hull of a semigroup which is a semilattice of groups.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 6 , December 1974 , pp. 1520 - 1536
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Petrich, Mario, The translational hull in semigroups and rings, Semigroup Forum 1 (1970), 283–360.Google Scholar
2. Petrich, Mario, On ideals of a semilattice, Czechoslovak Math. J. 22 (97) (1972), 361–367.Google Scholar
3. Petrich, Mario, Regular semigroups satisfying certain conditions on idempotent and ideals, Trans. Amer. Math. Soc. 179 (1972), 245–267.Google Scholar
4. Petrich, Mario, Introduction to semigroups (Merrill, Columbus, Ohio, 1973).Google Scholar
5. Petrich, Mario, Venveloppe de translations d'un demi-treillis de groupes, Can. J. Math. 25 (1973), 164–177.Google Scholar
6. Petrich, Mario, Regular semigroups which are subdirect products of a band and a semilattice of groups, Glasgow Math. J. 14 (1973), 27–49.Google Scholar
7. Petrich, Mario, The structure of completely regular semigroups, Trans. Amer. Math. Soc. 189 (1974), 211–236.Google Scholar