# ∏-COHERENT DIMENSIONS AND ∏-COHERENT RINGS

• Mao, Lixin
• Published : 2007.05.31
• 67 8

#### Abstract

R is called a right ${\Pi}-coherent$ ring in case every finitely generated torsion less 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

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#### Cited by

1. PRECOVERS AND PREENVELOPES BY MODULES OF FINITE FGT-INJECTIVE AND FGT-FLAT DIMENSIONS vol.25, pp.4, 2010, https://doi.org/10.4134/CKMS.2010.25.4.497
2. FGT-injective dimensions of Π-coherent rings and almost excellent extension vol.120, pp.2, 2010, https://doi.org/10.1007/s12044-010-0025-0