Volume 37 • Number 3 • 2014   • Relative Projective Dimensions Baiyu Ouyang, Luling Duan and Weiqing Li Abstract. In $(n,d)$-ring and $n$-coherent ring theory, $n$-presented modules plays an important role. In this paper, we firstly give some new characterizations of $n$-presented modules and $n$-coherent rings. Then, we introduce the concept of $(n,0)$-projective dimension, which measures how far away a finitely generated module is from being $n$-presented and how far away a ring is from being Noetherian, for modules and rings. This dimension has nice properties when the ring in question is $n$-coherent. Some known results are extended or obtained as corollaries. 2010 Mathematics Subject Classification: 16D10, 16E40 Full text: PDF