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Communications in Algebra Volume 51, 2023 - Issue 12
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Research Article

On modules and rings having large absolute direct summands

Trang Dao Thia Faculty of Applied Sciences, Ho Chi Minh City University of Industry and Trade (HUIT), Ho Chi Minh City, VietnamView further author information
,
Tamer M. Koşanb Department of Mathematics, Faculty of Sciences, Gazi University, Ankara, TurkeyView further author information
,
Özgür Taşdemirc Department of Business Administration, Trakya University, Faculty of Economics and Administrative Sciences, Balkan Campus, Edirne, TurkeyView further author information
&
Quynh Truong Congd Department of Mathematics, The University of Danang - University of Science and Education, Danang City, VietnamCorrespondence[email protected]
View further author information
Pages 4949-4961 | Received 23 May 2022, Accepted 05 Jun 2023, Published online: 21 Jun 2023

References

  • Alahmadi, A., Jain, S. K., Leroy, A. (2012). ADS modules. J. Algebra 352:215–222. DOI: 10.1016/j.jalgebra.2011.10.035.
  • Anderson, F. W., Fuller, K. R. (1974). Rings and Categories of Modules. New York: Springer-Verlag.
  • Burgess, W. D., Raphael, R. (1993). On Modules with The Absolute Direct Summand Property, Ring Theory, 137–148, Granville, OH, 1992. River Edge: World Scientific Publishing.
  • D’este, G., Tütüncü, D. K., Tribak, R. (2021) D3-modules versus D4-modules-applications to quivers. Glasgow Math. J. 63(3):697–723. DOI: 10.1017/S0017089520000452.
  • Dung, N. V., Huynh, D. V., Smith, P. F., Wisbauer, R. (1994). Extending Modules. Pitman Research Notes in Mathematics, 313. Harlow, New York: Longman.
  • Fuchs, L. (1970). Infinite Abelian Groups, vol. I. Pure and Applied Mathematics, Ser. Monogr. Textb., Vol. 36. New York, San Francisco, London: Academic Press.
  • Ibrahim, Y., Yousif, M. (2021). U-Modules with transitive perspectivity. Commun. Algebra 49(10):4501–4512. DOI: 10.1080/00927872.2021.1922699.
  • Kado, J., Kuratomi, Y., Oshiro, K. (2001). CS-property of direct sums of uniform modules. In: International Symposium on Ring Theory. Boston, MA: Birkhäuser, pp. 149–159.
  • Kasch, F., Mader, A. (2009). Regularity and Substructures of Hom. Basel: Frontiers in Mathematics.
  • Koşan, M. T., Quynh, T. C., Zemlicka, J. (2019). Essentially ADS modules and rings. In: Rings, Modules and Codes. Contemporary Mathematics, 727. Providence, RI: American Mathematical Society, pp. 223–236.
  • Lee, T. K., Zhou Y. (2013). Modules which are invariant under automorphisms of their injective hulls. J. Algebra Appl. 12(2):1250159. DOI: 10.1142/S0219498812501599.
  • Mohammed, S. H., Müller, B. J. (1990). Continous and Discrete Modules. London Mathematical Society Lecture Note, 147. Cambridge: Cambridge University Press.
  • Nicholson, W. K., Yousif, M. F. (2003). Quasi-Frobenius rings. Cambridge: Cambridge University Press.
  • Ozcan, A. C., Harmanci, A., Smith, P. F. (2006). Duo modules. Glasgow Math. J. 48(3):533–545. DOI: 10.1017/S0017089506003260.
  • Nicholson, W. K., Zhou, Y. (2006). Semiregular morphism. Commun. Algebra 34:219–233. DOI: 10.1080/00927870500346214.
  • Quynh, T. C., Koşan, M. T. (2014). On ADS modules and rings. Commun. Algebra 42(8):3541–3551. DOI: 10.1080/00927872.2013.788185.
  • Quynh, T. C., Abyzov, A., Ha, N. T. T., Yildirim, T. (2019). Modules close to the automorphism-invariant and coinvariant. J. Algebra Appl. 18(12):1950235. DOI: 10.1142/S0219498819502359.
  • Quynh, T. C., Koşan, M. T., Thuyet, L. V. (2013) On (semi)regular morphisms. Commun. Algebra 41:2933–2947. DOI: 10.1080/00927872.2012.667855.
  • Rizvi, S. T., Yousif, M. F. (1989). On continuous and singular modules. In: Non-commutative Ring Theory, Proceedings, Athens, OH, Lecture Notes in Mathematics 1448. Heidelberg: Springer-Verlag, pp. 116–124.
  • Santa-Clara, C. (1998). Some generalizations of injectivity. PhD thesis. University of Glasgow.
  • Tütüncü, D. K., Kuratomi, Y., Shibata, Y. (2019). On image summand coinvariant modules and kernel summand invariant modules. Turkish J. Math. 43(3):1456–1473. DOI: 10.3906/mat-1808-40.
  • Tütüncü, D. K., Kuratomi, Y. (2013). On mono-injective modules and mono-objective modules. Math. J. Okayama Univ. 55:117–129.
  • Wisbauer, R. (1991). Foundations of Module and Ring Theory. Reading: Gordon and Breach.

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