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A NOTE ON AUTOMORPHISM LIFTABLE MODULES

Yıl 2019, Cilt: 26 Sayı: 26, 111 - 121, 11.07.2019
https://doi.org/10.24330/ieja.587002

Öz

A module M is said to be an automorphism liftable module if
for each submodule N of M, every automorphism of the quotient M=N can
be lifted to an endomorphism of M. In this work, some properties of auto-
morphism liftable modules are investigated. Also, characterization for some
special rings such as perfect, semiperfect and uniserial are given by using au-
tomorphism liftable modules.

Kaynakça

  • A. N. Abyzov, T. C. Quynh and D. D. Tai, Dual automorphism-invariant modules over perfect rings, Sib. Math. J., 58(5) (2017), 743-751.
  • A. N. Abyzov and C. Q. Truong, Lifting of automorphisms of factor modules, Comm. Algebra, 46(11) (2018), 5073-5082.
  • K. A. Byrd, Some characterizations of uniserial rings, Math. Ann., 186 (1970), 163-170.
  • L. Fuchs and K. M. Rangaswamy, Quasi-projective abelian groups, Bull. Soc. Math. France, 98 (1970), 5-8.
  • J. S. Golan, Characterization of rings using quasiprojective modules, Israel J. Math., 8 (1970), 34-38.
  • J. S. Golan, Characterization of rings using quasiprojective modules II, Proc. Amer. Math. Soc., 28(2) (1971), 337-343.
  • S. M. Kaye, Ring theoretic properties of matrix rings, Canad. Math. Bull., 10 (1967), 365-374.
  • M. T. Kosan, N. T. T. Ha and T. C. Quynh, Rings for which every cyclic module is dual automorphism-invariant, J. Algebra Appl., 15(5) (2016), 1650078 (11 pp).
  • 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).
  • X. H. Nguyen, M. F. Yousif and Y. Zhou, Rings whose cyclics are D3-modules, J. Algebra Appl., 16(10) (2017), 1750184 (15 pp).
  • C. Selvaraj and S. Santhakumar, A note on dual automorphism invariant modules, J. Algebra Appl., 16(2) (2017), 1750024 (11 pp).
  • C. Selvaraj and S. Santhakumar, Automorphism liftable modules, Comment. Math. Univ. Carolin., 59(1) (2018), 35-44.
  • S. Singh and A. K. Srivastava, Dual automorphism-invariant modules, J. Algebra, 371 (2012), 262-275.
  • A. A. Tuganbaev, Automorphisms of submodules and their extensions, Discrete Math. Appl., 23(1) (2013), 115-124.
  • L. E. T. Wu and J. P. Jans, On quasi projectives, Illinois. J. Math., 11 (1967), 439-448.
Yıl 2019, Cilt: 26 Sayı: 26, 111 - 121, 11.07.2019
https://doi.org/10.24330/ieja.587002

Öz

Kaynakça

  • A. N. Abyzov, T. C. Quynh and D. D. Tai, Dual automorphism-invariant modules over perfect rings, Sib. Math. J., 58(5) (2017), 743-751.
  • A. N. Abyzov and C. Q. Truong, Lifting of automorphisms of factor modules, Comm. Algebra, 46(11) (2018), 5073-5082.
  • K. A. Byrd, Some characterizations of uniserial rings, Math. Ann., 186 (1970), 163-170.
  • L. Fuchs and K. M. Rangaswamy, Quasi-projective abelian groups, Bull. Soc. Math. France, 98 (1970), 5-8.
  • J. S. Golan, Characterization of rings using quasiprojective modules, Israel J. Math., 8 (1970), 34-38.
  • J. S. Golan, Characterization of rings using quasiprojective modules II, Proc. Amer. Math. Soc., 28(2) (1971), 337-343.
  • S. M. Kaye, Ring theoretic properties of matrix rings, Canad. Math. Bull., 10 (1967), 365-374.
  • M. T. Kosan, N. T. T. Ha and T. C. Quynh, Rings for which every cyclic module is dual automorphism-invariant, J. Algebra Appl., 15(5) (2016), 1650078 (11 pp).
  • 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).
  • X. H. Nguyen, M. F. Yousif and Y. Zhou, Rings whose cyclics are D3-modules, J. Algebra Appl., 16(10) (2017), 1750184 (15 pp).
  • C. Selvaraj and S. Santhakumar, A note on dual automorphism invariant modules, J. Algebra Appl., 16(2) (2017), 1750024 (11 pp).
  • C. Selvaraj and S. Santhakumar, Automorphism liftable modules, Comment. Math. Univ. Carolin., 59(1) (2018), 35-44.
  • S. Singh and A. K. Srivastava, Dual automorphism-invariant modules, J. Algebra, 371 (2012), 262-275.
  • A. A. Tuganbaev, Automorphisms of submodules and their extensions, Discrete Math. Appl., 23(1) (2013), 115-124.
  • L. E. T. Wu and J. P. Jans, On quasi projectives, Illinois. J. Math., 11 (1967), 439-448.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

S. Santhakumar Bu kişi benim

Yayımlanma Tarihi 11 Temmuz 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 26 Sayı: 26

Kaynak Göster

APA Santhakumar, S. (2019). A NOTE ON AUTOMORPHISM LIFTABLE MODULES. International Electronic Journal of Algebra, 26(26), 111-121. https://doi.org/10.24330/ieja.587002
AMA Santhakumar S. A NOTE ON AUTOMORPHISM LIFTABLE MODULES. IEJA. Temmuz 2019;26(26):111-121. doi:10.24330/ieja.587002
Chicago Santhakumar, S. “A NOTE ON AUTOMORPHISM LIFTABLE MODULES”. International Electronic Journal of Algebra 26, sy. 26 (Temmuz 2019): 111-21. https://doi.org/10.24330/ieja.587002.
EndNote Santhakumar S (01 Temmuz 2019) A NOTE ON AUTOMORPHISM LIFTABLE MODULES. International Electronic Journal of Algebra 26 26 111–121.
IEEE S. Santhakumar, “A NOTE ON AUTOMORPHISM LIFTABLE MODULES”, IEJA, c. 26, sy. 26, ss. 111–121, 2019, doi: 10.24330/ieja.587002.
ISNAD Santhakumar, S. “A NOTE ON AUTOMORPHISM LIFTABLE MODULES”. International Electronic Journal of Algebra 26/26 (Temmuz 2019), 111-121. https://doi.org/10.24330/ieja.587002.
JAMA Santhakumar S. A NOTE ON AUTOMORPHISM LIFTABLE MODULES. IEJA. 2019;26:111–121.
MLA Santhakumar, S. “A NOTE ON AUTOMORPHISM LIFTABLE MODULES”. International Electronic Journal of Algebra, c. 26, sy. 26, 2019, ss. 111-2, doi:10.24330/ieja.587002.
Vancouver Santhakumar S. A NOTE ON AUTOMORPHISM LIFTABLE MODULES. IEJA. 2019;26(26):111-2.