Research Article
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On Proper Class Coprojectively Generated by Modules With Projective Socle

Year 2020, Issue: 32, 79 - 87, 30.09.2020

Abstract

Let $\varepsilon$ : 0 --> A -->f B -->g C --> 0 be a short exact sequence of modules and module homomorphism. $\varepsilon$ is called gd-closed sequence if Imf is gd-closed in B. In this paper, the proper class $GD$− Closed, which is coprojectively generated by modules with projective socle, be studied and also its relations among Neat, Closed, $D$−Closed, $S$−Closed be investigated. Additionally, we examine coprojective modules of this class.                                                                 

                                                                                                                                                                                                                                                                      .

Supporting Institution

Research Fund of the Cukurova University.

Project Number

Project number: 12308

References

  • N.V. Dung, D.V. Huynh, P.F. Smith, R. Wisbauer, Extending modules, Pitman Research Notes in Math. Ser. 313 Longman Scientific and Technical, Harlow, 1994.
  • E. Büyükaşık, Y. Durgun, Neat-flat Modules, Comm. Algebra 44 (2016) 416-428.
  • E. Büyükaşık, Y. Durgun, Absolutely s-pure modules and neat-flat modules, Comm. Algebra 43 (2)(2015) 384-399.
  • A. David Buchsbaum, A note on homology in categories, Ann. of Math. (69) (2) (1959) 66-74.
  • J. Clark, C. Lomp, N. Vanaja, and R. Wisbauer, Lifting modules, Birkh¨auser Verlag, Basel, 2006.
  • S. Crivei, S.S¸ahinkaya, Modules whose closed submodules with essential socle are direct summands, Taiwanese J. Math. 18(4)(2014) 989-1002.
  • Y. Durgun, A. Çobankaya, On subprojectivity domains of g-semiartinian modules, J. Algebra Appl. (2021) https://doi.org/10.1142/S021949882150119X, (in press).
  • Y. Durgun, A. Çobankaya, Proper classes generated by t-closed submodules, An. S¸t. Univ. Ovidius Constanta 27 (2019) 83-95.
  • Y. Durgun, A. Çobankaya, G-Dickson Torsion Theory, International Science, Mathematics and Engineering Sciences Congress (2019) 978-983.
  • P. M. Cohn, On the free product of associative rings Math. Z. 71(1959) 380-398.
  • Y. Durgun, S. Özdemir, On S-Closed Submodules, J. Korean Math. Soc. 54 (2017) 1281-1299.
  • Y. Durgun, S. Özdemir, On D-Closed Submodules, Proc. Indian Acad. Sci (Math. Sci.) 130 (1)(2020) 14pp.
  • Y. Durgun, D-Extending Modules, Hacet. J. Math. Stat. (49)(2020) 1-7, https://doi.org/10.15672/hujms. 460241.
  • E. E. Enochs, O. M. G. Jenda, Relative Homological Algebra Walter de Gruyter, Berlin-New York, 2000.
  • L. Fuchs, Neat submodules over integral domains, Period. Math. Hungar. 64(2)(2012) 131-143.
  • K.R. Goodearl, Singular torsion and the splitting properties, Amer. Math. Soc. 124 , Providence, R. I. 1972.
  • A. I. Generalov, On weak and !-high purities in the category of modules, Mat. Sb. (N.S.) 105(147)(3) (1978), 389-402.
  • Y. Kara, A. Tercan, When some complement of a z-closed submodule is a summand, Comm. Algebra, 46(7)(2018) 3071-3078.
  • Kepka, T., On one class of purities, Comment. Math. Univ. Carolinae, 14 (1973), 139-154.
  • W.K. Nicholson, J.F. Watters, Rings with projective socle, Proc. Amer. Math. Soc., 102 (1988) 443-450.
  • G. Renault, ´Etude de certains anneaux li´es aux sous-modules compl´ements d’un A-module, C. R. Acad. Sci. Paris 259 (1964) 4203-4205.
  • J. Rotman, An Introduction to Homological Algebra, Universitext, Springer-Verlag, New York, 2009.
  • E.G. Skljarenko, Relative homological algebra in the category of modules, Russian Math. Surveys, 333(201) (1978) 85-120.
  • H. Z¨oschinger, Schwach-Flache Moduln. Comm. Algebra 41 (12) (2013) 4393-4407.
Year 2020, Issue: 32, 79 - 87, 30.09.2020

Abstract

Project Number

Project number: 12308

References

  • N.V. Dung, D.V. Huynh, P.F. Smith, R. Wisbauer, Extending modules, Pitman Research Notes in Math. Ser. 313 Longman Scientific and Technical, Harlow, 1994.
  • E. Büyükaşık, Y. Durgun, Neat-flat Modules, Comm. Algebra 44 (2016) 416-428.
  • E. Büyükaşık, Y. Durgun, Absolutely s-pure modules and neat-flat modules, Comm. Algebra 43 (2)(2015) 384-399.
  • A. David Buchsbaum, A note on homology in categories, Ann. of Math. (69) (2) (1959) 66-74.
  • J. Clark, C. Lomp, N. Vanaja, and R. Wisbauer, Lifting modules, Birkh¨auser Verlag, Basel, 2006.
  • S. Crivei, S.S¸ahinkaya, Modules whose closed submodules with essential socle are direct summands, Taiwanese J. Math. 18(4)(2014) 989-1002.
  • Y. Durgun, A. Çobankaya, On subprojectivity domains of g-semiartinian modules, J. Algebra Appl. (2021) https://doi.org/10.1142/S021949882150119X, (in press).
  • Y. Durgun, A. Çobankaya, Proper classes generated by t-closed submodules, An. S¸t. Univ. Ovidius Constanta 27 (2019) 83-95.
  • Y. Durgun, A. Çobankaya, G-Dickson Torsion Theory, International Science, Mathematics and Engineering Sciences Congress (2019) 978-983.
  • P. M. Cohn, On the free product of associative rings Math. Z. 71(1959) 380-398.
  • Y. Durgun, S. Özdemir, On S-Closed Submodules, J. Korean Math. Soc. 54 (2017) 1281-1299.
  • Y. Durgun, S. Özdemir, On D-Closed Submodules, Proc. Indian Acad. Sci (Math. Sci.) 130 (1)(2020) 14pp.
  • Y. Durgun, D-Extending Modules, Hacet. J. Math. Stat. (49)(2020) 1-7, https://doi.org/10.15672/hujms. 460241.
  • E. E. Enochs, O. M. G. Jenda, Relative Homological Algebra Walter de Gruyter, Berlin-New York, 2000.
  • L. Fuchs, Neat submodules over integral domains, Period. Math. Hungar. 64(2)(2012) 131-143.
  • K.R. Goodearl, Singular torsion and the splitting properties, Amer. Math. Soc. 124 , Providence, R. I. 1972.
  • A. I. Generalov, On weak and !-high purities in the category of modules, Mat. Sb. (N.S.) 105(147)(3) (1978), 389-402.
  • Y. Kara, A. Tercan, When some complement of a z-closed submodule is a summand, Comm. Algebra, 46(7)(2018) 3071-3078.
  • Kepka, T., On one class of purities, Comment. Math. Univ. Carolinae, 14 (1973), 139-154.
  • W.K. Nicholson, J.F. Watters, Rings with projective socle, Proc. Amer. Math. Soc., 102 (1988) 443-450.
  • G. Renault, ´Etude de certains anneaux li´es aux sous-modules compl´ements d’un A-module, C. R. Acad. Sci. Paris 259 (1964) 4203-4205.
  • J. Rotman, An Introduction to Homological Algebra, Universitext, Springer-Verlag, New York, 2009.
  • E.G. Skljarenko, Relative homological algebra in the category of modules, Russian Math. Surveys, 333(201) (1978) 85-120.
  • H. Z¨oschinger, Schwach-Flache Moduln. Comm. Algebra 41 (12) (2013) 4393-4407.
There are 24 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Ayşe Çobankaya 0000-0002-9017-1465

Project Number Project number: 12308
Publication Date September 30, 2020
Submission Date July 4, 2020
Published in Issue Year 2020 Issue: 32

Cite

APA Çobankaya, A. (2020). On Proper Class Coprojectively Generated by Modules With Projective Socle. Journal of New Theory(32), 79-87.
AMA Çobankaya A. On Proper Class Coprojectively Generated by Modules With Projective Socle. JNT. September 2020;(32):79-87.
Chicago Çobankaya, Ayşe. “On Proper Class Coprojectively Generated by Modules With Projective Socle”. Journal of New Theory, no. 32 (September 2020): 79-87.
EndNote Çobankaya A (September 1, 2020) On Proper Class Coprojectively Generated by Modules With Projective Socle. Journal of New Theory 32 79–87.
IEEE A. Çobankaya, “On Proper Class Coprojectively Generated by Modules With Projective Socle”, JNT, no. 32, pp. 79–87, September 2020.
ISNAD Çobankaya, Ayşe. “On Proper Class Coprojectively Generated by Modules With Projective Socle”. Journal of New Theory 32 (September 2020), 79-87.
JAMA Çobankaya A. On Proper Class Coprojectively Generated by Modules With Projective Socle. JNT. 2020;:79–87.
MLA Çobankaya, Ayşe. “On Proper Class Coprojectively Generated by Modules With Projective Socle”. Journal of New Theory, no. 32, 2020, pp. 79-87.
Vancouver Çobankaya A. On Proper Class Coprojectively Generated by Modules With Projective Socle. JNT. 2020(32):79-87.


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