Cleft extensions for quasi-entwining structures
J. N. Alonso Álvarez, J. M. Fernández Vilaboa, Ramón González Rodríguez · Mathematica Slovaca · 2018
Abstract In this paper we introduce the notions of quasi-entwining structure and cleft extension for a quasi-entwining structure. We prove that if (A, C, ψ) is a quasi-entwining structure and the associated extension to the submagma of coinvariants AC is cleft, there exists an isomorphism ωA between AC ⊗ C and A. Moreover, we define two unital but not necessarily associative products on AC ⊗ C. For these structures we obtain the necessary and sufficient conditions to assure that ωA is a magma isomorphism, giving some examples fulfilling these conditions.