JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (8): 85-89.doi: 10.6040/j.issn.1671-9352.0.2016.386

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Homological dimensions with respect to semidualizing modules and excellent extensions

CHEN Xiu-li1, CHEN Jian-long2   

  1. 1. Department of Basic Courses, Zhejiang University of Water Resources and Electric Power, Hangzhou 310018, Zhejiang, China;
    2. Department of Mathematics, Southeast University, Nanjing 210096, Jiangsu, China
  • Received:2016-08-22 Online:2017-08-20 Published:2017-08-03

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Abstract: Let C be a semidualizing R-module with R being a commutative ring. It is investigated the transfer properties of C-homological dimensions under(almost)excellent extensions, and it is discussed that the precovering and preenveloping properties of the C-projectives, C-injectives, and C-flats. As applications, it is proved that if S≥R is an excellent extension, then R is Noetherian if and only if S is Noetherian, and R is coherent if and only if S is coherent.

Key words: C-homological dimensions, coherent ring, Noetherian ring, semidualizing module, excellent extension

CLC Number: 

  • O153.3
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