Research Article
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Year 2018, Volume 23, Issue 23, 143 - 152, 11.01.2018
https://doi.org/10.24330/ieja.373656

Abstract

References

  • M. Alkan and A. Harmanci, On summand sum and summand intersection property of modules, Turkish J. Math., 26(2) (2002), 131-147.
  • V. Camillo, Y. Ibrahim, M. Yousif and Y. Zhou, Simple-direct-injective mod- ules, J. Algebra, 420 (2014), 39-53.
  • H. Q. Dinh, A note on pseudo-injective modules, Comm. Algebra, 33(2) (2005), 361-369.
  • N. Er, S. Singh and A. K. Srivastava, Rings and modules which are stable under automorphisms of their injective hulls, J. Algebra, 379 (2013), 223-229.
  • J. L. Garcia, Properties of direct summands of modules, Comm. Algebra, 17(1) (1989), 73-92.
  • A. W. Goldie, Torsion-free modules and rings, J. Algebra, 1 (1964), 268-287.
  • G. Lee, S. T. Rizvi and C. S. Roman, Dual Rickart modules, Comm. Algebra, 39(11) (2011), 4036-4058.
  • T. K. Lee and Y. Zhou, Modules which are invariant under automorphisms of their injective hulls, J. Algebra Appl., 12(2) (2013), 1250159 (9 pp).
  • S. H. Mohamed and B. J. Muller, Continuous and Discrete Modules, London Mathematical Society Lecture Note Series, 147, Cambridge University Press, Cambridge, 1990.
  • W. K. Nicholson, Semiregular modules and rings, Canad. J. Math., 28(5) (1976), 1105-1120.
  • W. K. Nicholson and Y. Zhou, Semiregular morphisms, Comm. Algebra, 34(1) (2006), 219-233.
  • B. L. Osofsky, Rings all of whose nitely generated modules are injective, Paci c J. Math., 14 (1964), 645-650.
  • B. L. Osofsky and P. F. Smith, Cyclic modules whose quotients have all com- plement submodules direct summands, J. Algebra, 139(2) (1991), 342-354.
  • V. S. Ramamurthi and K. M. Rangaswamy, On nitely injective modules, J. Austral. Math. Soc., 16 (1973), 239-248.
  • Y. Utumi, On continuous rings and self injective rings, Trans. Amer. Math. Soc., 118 (1965), 158-173.
  • R. Wisbauer, Foundations of Module and Ring Theory, Algebra, Logic and Applications, 3, Gordon and Breach Science Publishers, Philadelphia, PA, 1991.

Finite-direct-injective modules

Year 2018, Volume 23, Issue 23, 143 - 152, 11.01.2018
https://doi.org/10.24330/ieja.373656

Abstract

In this paper, we generalize the concept of direct-injective modules
to fi nite-direct-injective modules. Various basic properties of these modules are
studied. We show that the class of fi nite-direct-injective modules lies between
the class of direct-injective modules and the class of simple-direct-injective
modules. Also, we characterize semisimple artinian rings, V -rings and regular
rings in terms of fi nite-direct-injective modules.

References

  • M. Alkan and A. Harmanci, On summand sum and summand intersection property of modules, Turkish J. Math., 26(2) (2002), 131-147.
  • V. Camillo, Y. Ibrahim, M. Yousif and Y. Zhou, Simple-direct-injective mod- ules, J. Algebra, 420 (2014), 39-53.
  • H. Q. Dinh, A note on pseudo-injective modules, Comm. Algebra, 33(2) (2005), 361-369.
  • N. Er, S. Singh and A. K. Srivastava, Rings and modules which are stable under automorphisms of their injective hulls, J. Algebra, 379 (2013), 223-229.
  • J. L. Garcia, Properties of direct summands of modules, Comm. Algebra, 17(1) (1989), 73-92.
  • A. W. Goldie, Torsion-free modules and rings, J. Algebra, 1 (1964), 268-287.
  • G. Lee, S. T. Rizvi and C. S. Roman, Dual Rickart modules, Comm. Algebra, 39(11) (2011), 4036-4058.
  • T. K. Lee and Y. Zhou, Modules which are invariant under automorphisms of their injective hulls, J. Algebra Appl., 12(2) (2013), 1250159 (9 pp).
  • S. H. Mohamed and B. J. Muller, Continuous and Discrete Modules, London Mathematical Society Lecture Note Series, 147, Cambridge University Press, Cambridge, 1990.
  • W. K. Nicholson, Semiregular modules and rings, Canad. J. Math., 28(5) (1976), 1105-1120.
  • W. K. Nicholson and Y. Zhou, Semiregular morphisms, Comm. Algebra, 34(1) (2006), 219-233.
  • B. L. Osofsky, Rings all of whose nitely generated modules are injective, Paci c J. Math., 14 (1964), 645-650.
  • B. L. Osofsky and P. F. Smith, Cyclic modules whose quotients have all com- plement submodules direct summands, J. Algebra, 139(2) (1991), 342-354.
  • V. S. Ramamurthi and K. M. Rangaswamy, On nitely injective modules, J. Austral. Math. Soc., 16 (1973), 239-248.
  • Y. Utumi, On continuous rings and self injective rings, Trans. Amer. Math. Soc., 118 (1965), 158-173.
  • R. Wisbauer, Foundations of Module and Ring Theory, Algebra, Logic and Applications, 3, Gordon and Breach Science Publishers, Philadelphia, PA, 1991.

Details

Journal Section Articles
Authors

Sanjeev Kumar MAURYA This is me


Ashok Ji GUPTA This is me

Publication Date January 11, 2018
Published in Issue Year 2018, Volume 23, Issue 23

Cite

Bibtex @research article { ieja373656, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {1710 Sokak, No:41, Batikent/Ankara}, publisher = {Abdullah HARMANCI}, year = {2018}, volume = {23}, number = {23}, pages = {143 - 152}, doi = {10.24330/ieja.373656}, title = {Finite-direct-injective modules}, key = {cite}, author = {Maurya, Sanjeev Kumar and Gupta, Ashok Ji} }
APA Maurya, S. K. & Gupta, A. J. (2018). Finite-direct-injective modules . International Electronic Journal of Algebra , 23 (23) , 143-152 . DOI: 10.24330/ieja.373656
MLA Maurya, S. K. , Gupta, A. J. "Finite-direct-injective modules" . International Electronic Journal of Algebra 23 (2018 ): 143-152 <https://dergipark.org.tr/en/pub/ieja/issue/33727/373656>
Chicago Maurya, S. K. , Gupta, A. J. "Finite-direct-injective modules". International Electronic Journal of Algebra 23 (2018 ): 143-152
RIS TY - JOUR T1 - Finite-direct-injective modules AU - Sanjeev KumarMaurya, Ashok JiGupta Y1 - 2018 PY - 2018 N1 - doi: 10.24330/ieja.373656 DO - 10.24330/ieja.373656 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 143 EP - 152 VL - 23 IS - 23 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.373656 UR - https://doi.org/10.24330/ieja.373656 Y2 - 2022 ER -
EndNote %0 International Electronic Journal of Algebra Finite-direct-injective modules %A Sanjeev Kumar Maurya , Ashok Ji Gupta %T Finite-direct-injective modules %D 2018 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 23 %N 23 %R doi: 10.24330/ieja.373656 %U 10.24330/ieja.373656
ISNAD Maurya, Sanjeev Kumar , Gupta, Ashok Ji . "Finite-direct-injective modules". International Electronic Journal of Algebra 23 / 23 (January 2018): 143-152 . https://doi.org/10.24330/ieja.373656
AMA Maurya S. K. , Gupta A. J. Finite-direct-injective modules. IEJA. 2018; 23(23): 143-152.
Vancouver Maurya S. K. , Gupta A. J. Finite-direct-injective modules. International Electronic Journal of Algebra. 2018; 23(23): 143-152.
IEEE S. K. Maurya and A. J. Gupta , "Finite-direct-injective modules", International Electronic Journal of Algebra, vol. 23, no. 23, pp. 143-152, Jan. 2018, doi:10.24330/ieja.373656

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