• Title of article

    Flatness properties of acts over semigroups

  • Author/Authors

    Laan, Valdis University of Tartu - Narva mnt 18 - Tartu, Estonia , Reimaa, Ülo University of Tartu - Narva mnt 18 - Tartu, Estonia , Tart, Lauri University of Tartu - Narva mnt 18 - Tartu, Estonia , Teor, Elery Hotel Tartu - Soola 3 - Tartu, Estonia

  • Pages
    34
  • From page
    59
  • To page
    92
  • Abstract
    In this paper we study flatness properties (pullback flatness, limit flatness, finite limit flatness) of acts over semigroups. These are defined by requiring preservation of certain limits from the functor of tensor multiplication by a given act. We give a description of firm pullback flat acts using Conditions (P) and (E). We also study pure epimorphisms and their connections to finitely presented acts and pullback flat acts. We study these flatness properties in the category of all acts, as well as in the category of unitary acts and in the category of firm acts, which arise naturally in the Morita theory of semigroups.
  • Keywords
    Act over semigroup , pullback flatness , finite limit flatness , pure epimorphism , finitely presentable act , firm act , sequence act
  • Journal title
    Categories and General Algebraic Structures with Applications
  • Serial Year
    2021
  • Record number

    2667977