On \((\aleph,U)\)-coherence of modules and rings. (Q1888706)

Let \(U\) be a flat right \(R\)-module and let \(\aleph\) be an infinite cardinal number. A left \(R\)-module \(M\) is called \((\aleph,U)\)-coherent if every finitely presented \(M\)-projective in \(\sigma[M]\) is \((\aleph,U)\)-finitely generated in \(\sigma[M]\). Using the methods of \textit{P. Loustaunau} [Commun. Algebra 17, No. 1, 197-215 (1989; Zbl 0664.16019)], \textit{L. Oyonarte} and \textit{B. Torrecillas} [ibid. 24, No. 4, 1389-1407 (1996; Zbl 0845.16003)], etc., products of certain right \(R\)-modules are \(R\)-flat modules. The concept of an \((\aleph,U)\)-coherent dimension is defined and studied.