Automorphism-invariant modules
Alahmadi, Adel ; Facchini, Alberto ; Khanh Tung, Nguyen
Rendiconti del Seminario Matematico della Università di Padova, Tome 134 (2015), p. 241-260 / Harvested from Numdam
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Publié le : 2015-01-01
@article{RSMUP_2015__133__241_0,
     author = {Alahmadi, Adel and Facchini, Alberto and Khanh Tung, Nguyen},
     title = {Automorphism-invariant modules},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     volume = {134},
     year = {2015},
     pages = {241-260},
     mrnumber = {3354953},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_2015__133__241_0}
}

Alahmadi, Adel; Facchini, Alberto; Khanh Tung, Nguyen. Automorphism-invariant modules. Rendiconti del Seminario Matematico della Università di Padova, Tome 134 (2015) pp. 241-260. http://gdmltest.u-ga.fr/item/RSMUP_2015__133__241_0/

[1]D. W. Anderson – K. R. Fuller, Rings and Categories of Modules, Second Edition, GTM 13, Springer-Verlag, 1992. | MR 1245487 | Zbl 0765.16001

[2]B. Brainerd – J. Lambek, On the ring of quotients of a boolean ring, Canad. Math. Bull., 2 (1959), pp. 25–29. | MR 101199 | Zbl 0085.26104

[3]T. T. Bumby, Modules which are isomorphic to submodules of each other, Arch. Math., 16 (1965), pp. 184–185. | MR 184973 | Zbl 0138.26702

[4]R. Camps – W. Dicks, On semilocal rings, Israel J. Math., 81 (1993), pp. 203–211. | MR 1231187 | Zbl 0802.16010

[5]H. Q. Dinh, A note on pseudo-injective modules, Comm. Algebra, 33 (2005), pp. 361–369. | MR 2124332 | Zbl 1077.16004

[6]N. Er – S. Singh – A. K. Srivastava, Rings and modules which are stable under automorphisms of their injective hulls, J. Algebra, 379 (2013), pp. 223–229. | MR 3019253 | Zbl 1287.16007

[7]A. Facchini, Module Theory. Endomorphism rings and direct sum decompositions in some classes of modules, Progress in Math. 167, Birkhäuser Verlag, 1998. Reprinted in Modern Birkhäuser Classics, Birkhäuser Verlag, 2010. | MR 1634015 | Zbl 0930.16001

[8]A. Facchini – D. Herbera, Local morphisms and modules with a semilocal endomorphism ring, Algebr. Represent. Theory, 9 (2006), pp. 403–422. | MR 2250654 | Zbl 1130.16014

[9]K. R. Goodearl, Von Neumann Regular Rings, Krieger, Malabar, 1991. | MR 1150975 | Zbl 0749.16001

[10]P. A. Guil Asensio – A. K. Srivastava, Additive unit representations in endomorphism rings and an extension of a result of Dickson and Fuller, in: Ring Theory and its Applications, Contemp. Math. 609, Amer. Math. Soc., Providence 2014, D. V. Huynh, et al., eds., pp. 117–121. | MR 3204355 | Zbl 1296.16003

[11]P. A. Guil Asensio – A. K. Srivastava, Automorphism-invariant modules satisfy the exchange property, J. Algebra, 388 (2013), pp. 101–106. | MR 3061680 | Zbl 1296.16002

[12]D. Khurana – A. K. Srivastava, Right self-injective rings in which every element is a sum of two units, J. Algebra Appl., 6 (2007), pp. 281–286. | MR 2316422 | Zbl 1116.16033

[13]T.-K. Lee – Y. Zhou, Modules which are invariant under automorphisms of their injective hulls, J. Algebra Appl., 12 (2013), 1250159, 9 pp. | MR 3005608 | Zbl 1263.16005

[14]Mai Hoang Bien, The endomorphism ring of a square-free injective module, Acta Math. Vietnamica 39(3) (2014), Online DOI 10.1007/s40306-014-0075-y. | MR 3412571

[15]S. H. Mohamed – B. J. Müller, Continuous and Discrete Modules, London Mathematical Society, Lecture Notes Series 147, Cambridge University Press, 1990. | MR 1084376 | Zbl 0701.16001

[16]W. K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc., 229 (1977), pp. 269–278. | MR 439876 | Zbl 0352.16006

[17]S. Singh – A. K. Srivastava, Rings of invariant module type and automorphism-invariant modules, in: Ring Theory and its Applications, Contemp. Math. 609, Amer. Math. Soc., Providence 2014, D. V. Huynh, et al., eds., pp. 299–311. | MR 3204368 | Zbl 1296.16006

[18]B. Stenström, Rings of quotients, Springer-Verlag, 1975. | MR 389953 | Zbl 0296.16001

[19]P. Vámos, 2-good rings, Quart. J. Math., 56 (2005), pp. 417–430. | MR 2161255 | Zbl 1156.16303