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http://dx.doi.org/10.4134/JKMS.2007.44.3.719

∏-COHERENT DIMENSIONS AND ∏-COHERENT RINGS  

Mao, Lixin (DEPARTMENT OF BASIC COURSES NANJING INSTITUTE OF TECHNOLOGY)
Publication Information
Journal of the Korean Mathematical Society / v.44, no.3, 2007 , pp. 719-731 More about this Journal
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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