| Title:
|
Automorphism liftable modules (English) |
| Author:
|
Selvaraj, Chelliah |
| Author:
|
Santhakumar, Sudalaimuthu |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
59 |
| Issue:
|
1 |
| Year:
|
2018 |
| Pages:
|
35-44 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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). (English) |
| Keyword:
|
dual automorphism invariant module |
| Keyword:
|
supplemented module |
| Keyword:
|
semisimple ring |
| Keyword:
|
perfect ring |
| Keyword:
|
summand sum property |
| MSC:
|
16D40 |
| MSC:
|
16L30 |
| MSC:
|
16W20 |
| idZBL:
|
Zbl 06890395 |
| idMR:
|
MR3783807 |
| DOI:
|
10.14712/1213-7243.2015.237 |
| . |
| Date available:
|
2018-04-17T13:42:30Z |
| Last updated:
|
2020-04-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147177 |
| . |
| Reference:
|
[1] Alkan M., Harmanci A.: On summand sum and summand intersection property of modules.Turkish J. Math. 26 (2002), 131–147. |
| Reference:
|
[2] Bass H.: Finitistic dimension and a homological generalization of semiprimary rings.Trans. Amer. Math. Soc. 95 (1960), 466–488. 10.1090/S0002-9947-1960-0157984-8 |
| Reference:
|
[3] Byrd K. A.: Some characterizations of uniserial rings.Math. Ann. 186 (1970), 163–170. 10.1007/BF01433274 |
| Reference:
|
[4] Garcia J. L.: Properties of direct summands of modules.Comm. Algebra 17 (1989), 73–92. 10.1080/00927878908823714 |
| Reference:
|
[5] Golan J. S.: Characterization of rings using quasiprojective modules.Israel J. Math. 8 (1970), 34–38. 10.1007/BF02771548 |
| Reference:
|
[6] Golan J. S.: Characterization of rings using quasiprojective modules II., Proc. Amer. Math. Soc. 28 (1971), no. 2, 337–343. 10.1090/S0002-9939-1971-0280551-5 |
| Reference:
|
[7] Golan J. S.: Characterization of rings using quasiprojective modules III., Proc. Amer. Math. Soc. 31 (1972), no. 2, 401–408. 10.1090/S0002-9939-1972-0302700-3 |
| Reference:
|
[8] Koşan M. T., Ha N. T. T., Quynh T. C.: Rings for which every cyclic module is dual automorphism-invariant.J. Algebra Appl. 15 (2016), no. 5, 1650078, 11 pp. 10.1142/S021949881650078X |
| Reference:
|
[9] Satyanarayana M.: Semisimple rings.Amer. Math. Monthly 74 (1967), 1086. 10.2307/2313615 |
| Reference:
|
[10] Selvaraj C., Santhakumar S.: A note on dual automorphism-invariant modules.J. Algebra Appl. 16 (2017), no. 2, 1750024, 11 pp. 10.1142/S0219498817500244 |
| Reference:
|
[11] Singh S., Srivastava A. K.: Dual automorphism-invariant modules.J. Algebra 371 (2012), 262–275. 10.1016/j.jalgebra.2012.08.012 |
| Reference:
|
[12] Tuganbaev A. A.: Automorphisms of submodules and their extensions.Discrete Math. Appl. 23 (2013), no. 1, 115–124. 10.1515/dma-2013-006 |
| Reference:
|
[13] Tütüncü D. K.: A note on ADS$^*$-modules.Bull. Math. Sci. 2 (2012), 359–363. 10.1007/s13373-012-0020-0 |
| Reference:
|
[14] Ware R.: Endomorphism rings of projective modules.Trans. Amer. Math. Soc. 155 (1971), 233–256. 10.1090/S0002-9947-1971-0274511-2 |
| . |
