Journal of the
Korean Mathematical Society JKMS

$R$ is called a right $\Pi$-coherent ring in case every finitely generated torsionless right $R$-module is finitely presented. In this paper, we define a dimension for rings, called $\Pi$-coherent dimension, which measures how far away a ring is from being $\Pi$-coherent. This dimension has nice properties when the ring in question is coherent. In addition, we study some properties of $\Pi$-coherent rings in terms of preenvelopes and precovers.

Keywords: $\Pi$-coherent dimension, $\Pi$-coherent ring, $FGT$-injective module, $FGT$-flat module, $FGT$-injective dimension, preenvelope, precover

MSC numbers: 16P70, 16D40, 16D50