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Perfect monoids revisited

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Abstract

A new characterization of perfect monoids, i.e., monoids over which every act has a projective cover, is given. As was shown by Fountain [1] a monoid is perfect if and only if all strongly flat acts over it are projective. Using our new condition, an alternative version is given of a recent result, of Liu [7] describing monoids over which all strongly flat right acts are projective generators, or are free.

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References

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Authors and Affiliations

  1. Institute of Pure Mathematics, University of Tartu, EE2400, Tartu, Estonia

    Mati Kilp

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  1. Mati Kilp
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Additional information

Communicated by J. M. Howie

This research has been supported by the Estonian Science Foundation, Grant No. 930.

I would like to thank the School of Mathematical and Computational Sciences of the University of St. Andrews for excellent working conditions.

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Kilp, M. Perfect monoids revisited. Semigroup Forum 53, 225–229 (1996). https://doi.org/10.1007/BF02574138

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  • DOI: https://doi.org/10.1007/BF02574138

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