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2 results

  • Perfection for semigroups

  • Part of
  • Valdis Laan, Alvin Lepik
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 66 / Issue 1 / February 2023
    Published online by Cambridge University Press:
    24 April 2023, pp. 259-287
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      • Open access
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  • We call a semigroup right perfect if every object in the category of unitary right acts over that semigroup has a projective cover. In this paper, we generalize results about right perfect monoids to the case of semigroups. In our main theorem, we will give nine conditions equivalent to right perfectness of a factorizable semigroup. We also prove that right perfectness is a Morita invariant for factorizable semigroups.

  • On the Projective Cover of an orbit space

  • Part of
  • K. K. Azad, Gunjan Agrawal
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 46 / Issue 2 / April 1989
    Published online by Cambridge University Press:
    09 April 2009, pp. 308-312
    Print publication:
    April 1989
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  • In this paper, we obtain the projective cover of the orbit space X/G in terms of the orbit space of the projective space of X, when X is a Tychonoff G-space and G is a finite discrete group. An example shows that finiteness of G is needed.