Abstract
In this paper, Gorenstein FI-flat complexes are introduced, and their characteristics are studied over a \(\mathcal {GFI}_{\mathcal {F}}\)-closed ring. Also this paper proves that every complex of R-modules has a Gorenstein FI-flat complex preenvelope over a \(\mathcal {GFI}_{\mathcal {F}}\)-closed ring.
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Auslander. M.: Anneaux de Gorenstein, et torsion en algebre commutative. Seminaire d’Algebre Commutative dirige par Pierre Samuel. Secretariat mathematique. Paris (1967)
Auslander. M and Bridger.M.: Stable Module Theory. Memoirs. Amer. Math. Soc. Vol. 94, Providence, RI: Amer. Math. Soc., (1969).
Meggiben. C.:Absolutely Pure modules, Proc. Amer. Math. Soc., 26, 561–566 (1970).
Rotman J. J.: An Introduction to Homological Algebra. Academic Press, 1979.
Enochs E.: Injective and flat covers, envelopes and resolvents. Israel J. of Math. 39 189–209 (1981).
Enochs E. and Lopez J.A.-Ramos: Kapalansky classes. Rend. Semin. Mat. Univ.Padova. 107, 67–79 (2002).
Holm H.: Gorenstein homological dimensions. J. Pure Appl. Algebra. 189, 167–193 (2004).
Mao L. and Ding N.: FI-injective and FI-flat modules. J. Algebra. 209, 367–385 (2007).
Enochs E.: Cartan-Eilenberg, complexes and resolutions. J.Algebra, 342,16–39 (2011).
Selvaraj C., Biju V. and Udhayakumar R.: Stability of Gorenstein F I-flat mod-ules. Far East J. of Math. 95, (2), 159–168 (2014).
Gangyang and Li Liang : Carten-Eilenberg Gorenstein Flat complexes. Math. Scand. 114, 5–25 (2014).
Selvaraj C., Biju V. and Udhayakumar R.: Gorenstein FI-flat (pre)covers. Gulf J. of Math. 3, 46–58 (2015).
Biju V. and Udhayakumar R.: FI-flat Resolutions and Dimensions. Global Journal of Pure and Applied Mathematics. 12, 808–811 (2016).
Selvaraj C., Biju V. and Udhayakumar R.: Gorenstein FI-flat Dimension and Tate Homology. Vietnam. J. Math. 44, 679–695 (2016).
Vasudevan B., Udhayakumar R. and Selvaraj C.: Gorenstein FI-flat dimension and Relative Homology. Afrika Matematika. 28, 1143–1156 (2017).
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Biju, V. (2018). Gorenstein FI-Flat Complexes and (Pre)envelopes. In: Madhu, V., Manimaran, A., Easwaramoorthy, D., Kalpanapriya, D., Mubashir Unnissa, M. (eds) Advances in Algebra and Analysis. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-01120-8_10
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DOI: https://doi.org/10.1007/978-3-030-01120-8_10
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Publisher Name: Birkhäuser, Cham
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