JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (8): 81-84.doi: 10.6040/j.issn.1671-9352.0.2016.432

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Characterizations of rings relative to an ideal

WANG Yong-duo, HE Jian*   

  1. School of Science, Lanzhou University of Technology, Lanzhou 730050, Gansu, China
  • Received:2016-09-18 Online:2017-08-20 Published:2017-08-03

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Abstract: Let I be an ideal of a ring R. The concept of pseudo semiprojective I-covers is introduced. It is shown that every left R-module has a pseudo semiprojective I-cover if and only if every left R-module has a proj-ective I-cover. It is also proved that the class of all pseudo semiprojective modules is a projectivity class, and then some well known results are generalized.

Key words: semiregular ring, pseudo semiprojective module, semiperfect ring, projectivity class

CLC Number: 

  • O152.7
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