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Year 2021, Volume: 4 Issue: 2, 83 - 87, 01.06.2021
https://doi.org/10.33401/fujma.869714

Abstract

References

  • [1] N. V. Dung, D. V. Huynh, P. F. Smith, R. Wisbauer, Extending Modules, Longman, Harlow, 1994.
  • [2] F. T. Mutlu, On matrix rings with the SIP and the Ads, Turk. J. Math., 42 (2018), 2657 – 2663.
  • [3] A. Tercan, C. C. Y¨ucel, Module theory extending modules and generalizations, Birkhauser, Basel, 2016.
  • [4] R. Yasşar, Modules in which semisimple fully invariant submodules are essential in summands, Turk. J. Math., 43(5) (2019), 2327-2336.
  • [5] G. F. Birkenmeier, Y. Kara, A. Tercan, p-Baer rings, J. Algebra App., 17(2) (2018), 1850029.
  • [6] G. F. Birkenmeier, A. Tercan, C. C. Y¨ucel, The extending condition relative to sets of submodules, Comm. Algebra, 42 (2014), 764-778.
  • [7] Y. Kara, On projective invariant semisimple submodules, Al-Qadisiyah J. Pure Sci., 26(1) (2020), 13-19.
  • [8] B. Zimmermann, W. Zimmermann, Classes of modules with the exchange property, J. Algebra, 88(2) (1984), 416-434.
  • [9] S. H. Mohamed, B. J. M¨uller, Continuous and Discrete Modules, Cambridge University Press, 1990.
  • [10] G. F. Birkenmeier, J. K. Park, S. T. Rizvi, Extensions of rings and modules, Birkhauser, New York, NY, USA, 2013.
  • [11] L. Fuchs, Infinite Abelian Groups I, Academic Press, New York, NY, USA, 1970.
  • [12] A. Tercan, Weak (C11) modules and algebraic topology type examples, Rocky Mount J. Math., 34(2) (2004), 783-792.
  • [13] I. Kaplansky, Rings of Operators, Benjamin, New York, NY, USA, 1968.

On Weak Projection Invariant Semisimple Modules

Year 2021, Volume: 4 Issue: 2, 83 - 87, 01.06.2021
https://doi.org/10.33401/fujma.869714

Abstract

We introduce and investigate the notion of weak projection invariant semisimple modules. We deal with the structural properties of this new class of modules. In this trend we have indecomposable decompositions of the special class of the former class of modules via some module theoretical properties. As a consequence, we obtain when the finite exchange property implies full exchange property for the latter class of modules.

References

  • [1] N. V. Dung, D. V. Huynh, P. F. Smith, R. Wisbauer, Extending Modules, Longman, Harlow, 1994.
  • [2] F. T. Mutlu, On matrix rings with the SIP and the Ads, Turk. J. Math., 42 (2018), 2657 – 2663.
  • [3] A. Tercan, C. C. Y¨ucel, Module theory extending modules and generalizations, Birkhauser, Basel, 2016.
  • [4] R. Yasşar, Modules in which semisimple fully invariant submodules are essential in summands, Turk. J. Math., 43(5) (2019), 2327-2336.
  • [5] G. F. Birkenmeier, Y. Kara, A. Tercan, p-Baer rings, J. Algebra App., 17(2) (2018), 1850029.
  • [6] G. F. Birkenmeier, A. Tercan, C. C. Y¨ucel, The extending condition relative to sets of submodules, Comm. Algebra, 42 (2014), 764-778.
  • [7] Y. Kara, On projective invariant semisimple submodules, Al-Qadisiyah J. Pure Sci., 26(1) (2020), 13-19.
  • [8] B. Zimmermann, W. Zimmermann, Classes of modules with the exchange property, J. Algebra, 88(2) (1984), 416-434.
  • [9] S. H. Mohamed, B. J. M¨uller, Continuous and Discrete Modules, Cambridge University Press, 1990.
  • [10] G. F. Birkenmeier, J. K. Park, S. T. Rizvi, Extensions of rings and modules, Birkhauser, New York, NY, USA, 2013.
  • [11] L. Fuchs, Infinite Abelian Groups I, Academic Press, New York, NY, USA, 1970.
  • [12] A. Tercan, Weak (C11) modules and algebraic topology type examples, Rocky Mount J. Math., 34(2) (2004), 783-792.
  • [13] I. Kaplansky, Rings of Operators, Benjamin, New York, NY, USA, 1968.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Ramazan Yaşar 0000-0001-6775-1069

Publication Date June 1, 2021
Submission Date January 28, 2021
Acceptance Date April 5, 2021
Published in Issue Year 2021 Volume: 4 Issue: 2

Cite

APA Yaşar, R. (2021). On Weak Projection Invariant Semisimple Modules. Fundamental Journal of Mathematics and Applications, 4(2), 83-87. https://doi.org/10.33401/fujma.869714
AMA Yaşar R. On Weak Projection Invariant Semisimple Modules. FUJMA. June 2021;4(2):83-87. doi:10.33401/fujma.869714
Chicago Yaşar, Ramazan. “On Weak Projection Invariant Semisimple Modules”. Fundamental Journal of Mathematics and Applications 4, no. 2 (June 2021): 83-87. https://doi.org/10.33401/fujma.869714.
EndNote Yaşar R (June 1, 2021) On Weak Projection Invariant Semisimple Modules. Fundamental Journal of Mathematics and Applications 4 2 83–87.
IEEE R. Yaşar, “On Weak Projection Invariant Semisimple Modules”, FUJMA, vol. 4, no. 2, pp. 83–87, 2021, doi: 10.33401/fujma.869714.
ISNAD Yaşar, Ramazan. “On Weak Projection Invariant Semisimple Modules”. Fundamental Journal of Mathematics and Applications 4/2 (June 2021), 83-87. https://doi.org/10.33401/fujma.869714.
JAMA Yaşar R. On Weak Projection Invariant Semisimple Modules. FUJMA. 2021;4:83–87.
MLA Yaşar, Ramazan. “On Weak Projection Invariant Semisimple Modules”. Fundamental Journal of Mathematics and Applications, vol. 4, no. 2, 2021, pp. 83-87, doi:10.33401/fujma.869714.
Vancouver Yaşar R. On Weak Projection Invariant Semisimple Modules. FUJMA. 2021;4(2):83-7.

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