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dual automorphism invariant module; supplemented module; semisimple ring; perfect ring; summand sum property
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).
[1] Alkan M., Harmanci A.: On summand sum and summand intersection property of modules. Turkish J. Math. 26 (2002), 131–147.
[2] Bass H.: Finitistic dimension and a homological generalization of semiprimary rings. Trans. Amer. Math. Soc. 95 (1960), 466–488. DOI 10.1090/S0002-9947-1960-0157984-8
[3] Byrd K. A.: Some characterizations of uniserial rings. Math. Ann. 186 (1970), 163–170. DOI 10.1007/BF01433274
[4] Garcia J. L.: Properties of direct summands of modules. Comm. Algebra 17 (1989), 73–92. DOI 10.1080/00927878908823714
[5] Golan J. S.: Characterization of rings using quasiprojective modules. Israel J. Math. 8 (1970), 34–38. DOI 10.1007/BF02771548
[6] Golan J. S.: Characterization of rings using quasiprojective modules II. Proc. Amer. Math. Soc. 28 (1971), no. 2, 337–343. DOI 10.1090/S0002-9939-1971-0280551-5
[7] Golan J. S.: Characterization of rings using quasiprojective modules III. Proc. Amer. Math. Soc. 31 (1972), no. 2, 401–408. DOI 10.1090/S0002-9939-1972-0302700-3
[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. DOI 10.1142/S021949881650078X
[9] Satyanarayana M.: Semisimple rings. Amer. Math. Monthly 74 (1967), 1086. DOI 10.2307/2313615
[10] Selvaraj C., Santhakumar S.: A note on dual automorphism-invariant modules. J. Algebra Appl. 16 (2017), no. 2, 1750024, 11 pp. DOI 10.1142/S0219498817500244
[11] Singh S., Srivastava A. K.: Dual automorphism-invariant modules. J. Algebra 371 (2012), 262–275. DOI 10.1016/j.jalgebra.2012.08.012
[12] Tuganbaev A. A.: Automorphisms of submodules and their extensions. Discrete Math. Appl. 23 (2013), no. 1, 115–124. DOI 10.1515/dma-2013-006
[13] Tütüncü D. K.: A note on ADS$^*$-modules. Bull. Math. Sci. 2 (2012), 359–363. DOI 10.1007/s13373-012-0020-0
[14] Ware R.: Endomorphism rings of projective modules. Trans. Amer. Math. Soc. 155 (1971), 233–256. DOI 10.1090/S0002-9947-1971-0274511-2
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