JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (12): 5-9.doi: 10.6040/j.issn.1671-9352.0.2017.219

Previous Articles     Next Articles

Simple dual Rickart modules

WANG Yong-duo, MA Ya-jun*   

  1. School of Science, Lanzhou University of Technology, Lanzhou 730050, Gansu, China
  • Received:2017-05-10 Online:2017-12-20 Published:2017-12-22

Abstract: The concept of simple dual Rickart modules is introduced. Its basic properties are studies and it is proved that a ring R is V-ring if and only if every right R-module is simple dual Rickart module.

Key words: simple dual Rickart module, simple-direct-injective module, regular ring, V-ring

CLC Number: 

  • O152.7
[1] LEE G Y, RIZVI S T, ROMAN C S. Dual Rickart modules[J]. Comm Algebra, 2011, 39(41):4036-4058.
[2] CAMILO V, IBRAHIM Y, YOUSIF M, et al. Simple-direct-injective modules[J]. J Algebra, 2014, 420:39-53.
[3] LEE G Y, RIZVI S T, ROMAN C S. Rickart modules[J]. Comm Algebra, 2010, 38:4005-4027.
[4] ANDERSON F W, FULLER K R. Rings and categories of modules: graduate texts in mathematics[M]. 2nd. New York: Springer, 1992.
[5] AMIN I, YOUSIF M, ZEYADA N. Soc-injective rings and modules[J]. Comm Algebra, 2005, 33:4229-4250.
[6] LAM T Y. Lectures on modules and rings[M]. New York: Springer, 1999.
[7] ROTMAN J J. An introduction to homological algebra[M]. New York: Academic Press, 1979.
[8] KASH F. Modules and rings[M] // London Math Soc Monogr, Vol 17. New York: Academic Press, 1982.
[9] AMIN I, IBRAHIM Y,YOUSIF M F. C3-modules[J]. Algebra Colloq, 2015, 22(4):655-670.
[10] DING Nanqing, IBRAHIM Y, ZHOU Yiqiang. C4-modules[J]. Comm Algebra, 2017, 45(4):1727-1740.
[1] WANG Yong-duo, HE Jian. Characterizations of rings relative to an ideal [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 81-84.
[2] ZHANG Zi-heng, CHU Mao-quan, YIN Xiao-bin. Some properties of GWCN rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(12): 10-16.
[3] LU Qi1, BAO Hong-wei1, LIANG Liang2. WGP-injectivity of rings#br# [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(06): 35-39.
[4] WU Guo-ying, WU Jun. On the strong regularity of J-rings [J]. J4, 2012, 47(2): 71-73.
[5] YIN Xiao-bin1, HUANG Xiao-lin1, WANG Kai-yun2. Endomorphism rings of quasi AP-injective modules [J]. J4, 2010, 45(6): 31-34.
[6] FENG Xiao,ZHANG Shun-hua* . Left G-regular rings [J]. J4, 2007, 42(8): 51-54 .
Full text



No Suggested Reading articles found!