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Regular principal factors in free objects in Rees-Sushkevich varieties

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Abstract

In a previous paper, the author showed how to associate a completely 0-simple semigroup with a connected bipartite graph containing labelled edges. In the main theorem, it is shown how these fundamental semigroups can be used to describe the regular principal factors of the free objects in certain Rees-Sushkevich varieties, namely, the varieties of semigroups that are generated by all completely 0-simple semigroups over groups in a variety of finite exponent. This approach is then used to solve the word problem for each of these varieties for which the corresponding group variety has solvable word problem.

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Acknowledgement

The author would like to thank Andrei Kelarev for his suggestions that led to many improvements to this paper.

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Authors and Affiliations

  1. Department of Mathematics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada

    Norman R. Reilly

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  1. Norman R. Reilly
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Correspondence to Norman R. Reilly.

Additional information

Communicated by Thomas E. Hall.

The author gratefully acknowledges the support of the Natural Sciences and Engineering Research Council of Canada.

The results contained in this paper were announced at the 3rd Novi Sad Algebraic Conference, Novi Sad, August 17–21, 2009.

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Reilly, N.R. Regular principal factors in free objects in Rees-Sushkevich varieties. Semigroup Forum 86, 162–182 (2013). https://doi.org/10.1007/s00233-012-9398-y

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  • DOI: https://doi.org/10.1007/s00233-012-9398-y

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