Automorphism liftable modules

Chelliah Selvaraj; Sudalaimuthu Santhakumar

Commentationes Mathematicae Universitatis Carolinae (2018)

  • Volume: 59, Issue: 1, page 35-44
  • ISSN: 0010-2628

Abstract

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We introduce the notion of an automorphism liftable module and give a characterization to it. We prove that category equivalence preserves automorphism liftable. Furthermore, we characterize semisimple rings, perfect rings, hereditary rings and quasi-Frobenius rings by properties of automorphism liftable modules. Also, we study automorphism liftable modules with summand sum property (SSP) and summand intersection property (SIP).

How to cite

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Selvaraj, Chelliah, and Santhakumar, Sudalaimuthu. "Automorphism liftable modules." Commentationes Mathematicae Universitatis Carolinae 59.1 (2018): 35-44. <http://eudml.org/doc/294427>.

@article{Selvaraj2018,
abstract = {We introduce the notion of an automorphism liftable module and give a characterization to it. We prove that category equivalence preserves automorphism liftable. Furthermore, we characterize semisimple rings, perfect rings, hereditary rings and quasi-Frobenius rings by properties of automorphism liftable modules. Also, we study automorphism liftable modules with summand sum property (SSP) and summand intersection property (SIP).},
author = {Selvaraj, Chelliah, Santhakumar, Sudalaimuthu},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {dual automorphism invariant module; supplemented module; semisimple ring; perfect ring; summand sum property},
language = {eng},
number = {1},
pages = {35-44},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Automorphism liftable modules},
url = {http://eudml.org/doc/294427},
volume = {59},
year = {2018},
}

TY - JOUR
AU - Selvaraj, Chelliah
AU - Santhakumar, Sudalaimuthu
TI - Automorphism liftable modules
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2018
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 59
IS - 1
SP - 35
EP - 44
AB - We introduce the notion of an automorphism liftable module and give a characterization to it. We prove that category equivalence preserves automorphism liftable. Furthermore, we characterize semisimple rings, perfect rings, hereditary rings and quasi-Frobenius rings by properties of automorphism liftable modules. Also, we study automorphism liftable modules with summand sum property (SSP) and summand intersection property (SIP).
LA - eng
KW - dual automorphism invariant module; supplemented module; semisimple ring; perfect ring; summand sum property
UR - http://eudml.org/doc/294427
ER -

References

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  11. Singh S., Srivastava A. K., 10.1016/j.jalgebra.2012.08.012, J. Algebra 371 (2012), 262–275. DOI10.1016/j.jalgebra.2012.08.012
  12. Tuganbaev A. A., 10.1515/dma-2013-006, Discrete Math. Appl. 23 (2013), no. 1, 115–124. DOI10.1515/dma-2013-006
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