View More View Less
  • 1 University of Tartu, Ülikooli 18, 50090 Tartu, Estonia
  • | 2 University of Tartu, Ülikooli 18, 50090 Tartu, Estonia
Restricted access

Purchase article

USD  $25.00

1 year subscription (Individual Only)

USD  $800.00

Abstract

We prove that in the category of firm acts over a firm semigroup monomorphisms co-incide with regular monomorphisms and we give an example of a non-injective monomorphism in this category. We also study conditions under which monomorphisms are injective and we prove that the lattice of subobjects of a firm act over a firm semigroup is isomorphic to the lattice unitary subacts of that act.

  • [1]

    Borceux, F., Handbook of Categorical Algebra 1: Basic Category Theory, Cambridge University Press, Cambridge, 1994.

  • [2]

    Bulman-Fleming, S. and McDowell, K., Absolutely flat semigroups, Pacific J. Math. 107 (1983), 319333.

  • [3]

    Bulman-Fleming, S. and McDowell, K., Left absolutely flat generalized inverse semigroups, Proc. Amer. Math. Soc. 94 (1985), 553561.

  • [4]

    Chen, Y. Q. and Shum, K. P. Morita equivalence for factorisable semigroups, Acta Math. Sin. (Engl. Ser.) 17 (2001), 437454.

  • [5]

    González-Férez, J. and Marín, L., Monomorphisms and kernels in the category of firm modules, Glasgow Math. J. 52A (2010), 8391.

  • [6]

    Kilp, M., Flat polygons, Tartu Riikl. Ül. Toimetised 253 (1970), 6672.

  • [7]

    Laan, V. and Márki, L., Fair semigroups and Morita equivalence, Semigroup Forum 92 (2016), 633644.

  • [8]

    Laan, V., Márki, L. and Reimaa, Ü., Morita equivalence of firm semigroups, manuscript.

  • [9]

    Lawson, M. V. Morita equivalence of semigroups with local units, J. Pure Appl. Algebra 215 (2011), 455á470.

  • [10]

    MacLane, S., Categories for the Working Mathematician, Springer, 1998.