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References
Alkan, M. and Özcan, A. C., Semiregular modules with respect to a fully invariant module, Comm. Algebra 32, 4285–4301, (2005).
Keskin, D., Supplemented modules and endomorphism rings, PhD Thesis, Hacettepe University, Ankara (1999).
Keskin, D., On lifting modules, Comm. Algebra 28, 3427–3440 (2000).
Lomp, Ch., On dual Goldie dimension, Diploma Thesis, University of Düsseldorf (1996).
Lomp, Ch., On semilocal modules and rings, Comm. Algebra 27, 1921–1935 (1999).
Mohamed, S. H. and Müller, B. J., Continuous and Discrete Modules, London Math. Soc. Lect. Notes Ser. 147, Cambridge Univ. Press, Cambridge (1990).
Nicholson, W. K., Semiregular modules and rings, Canad. J. Math. 28(5), 1105–1120 (1976).
Özcan, A. C. and Alkan, M., Semiperfect modules with respect to a preradical, Comm. Algebra, to appear.
Talebi, Y. and Vanaja, N., Copolyform modules, Comm. Algebra 30, 1461–1473 (2002).
Wisbauer, R., Foundations of Module and Ring Theory, Gordon and Breach, Reading (1991). Grundlagen der Modul-und Ringtheorie, Verlag Reinhard Fischer, München (1988).
Yousif, M. F. and Zhou, Yiqiang, Semiregular, semiperfect and perfect rings relative to an ideal, Rocky Mt. J. Math. 32, 1651–1671 (2002).
Zöschinger, H., Projektive Moduln mit endlich erzeugtem Radikalfaktormodul, Math. Ann. 255, 199–206 (1981).
References
Baba, Y. and Harada, M., On almost M-projectives and almost M-injectives, Tsukuba J. Math. 14, 53–69 (1990).
Hanada, K., Kuratomi, Y. and Oshiro, K., On direct sums of extending modules and internal exchange property, Proc. 32nd Symposium on Ring Theory and Representation Theory (Yamaguchi, 1999), 1–17, Tokyo Univ. Agric. Technol., Tokyo (2000).
Harada, M., On modules with lifting properties, Osaka J. Math. 19, 189–201 (1982).
Harada, M. and Mabuchi, T., On almost M-projectives, Osaka J. Math. 26, 837–848 (1989).
Harada, M. and Tozaki, A., Almost M-projectives and Nakayama rings, J. Algebra 122, 447–474 (1989).
Keskin, D., On lifting modules, Comm. Algebra 28, 3427–3440 (2000).
Kuratomi, Y., On direct sum of lifting modules and internal exchange property, Comm. Algebra 33, 1795–1804 (2005).
Mohamed, S. H. and Müller, B. J., Ojective modules, Comm. Algebra 30, 1817–1827 (2002).
Mohamed, S. H. and Müller, B. J., Cojective modules, J. Egyptian Math. Sci. 12, 83–96 (2004).
Orhan, N. and Keskin Tütüncü, D., Characterizations of lifting modules in terms of cojective modules and the class of \( \mathcal{B}\left( {\mathcal{M},\mathcal{X}} \right) \) , Int. J. Math. 16(6), 647–660 (2005).
References
Baba, Y. and Harada, M., On almost M-projectives and almost M-injectives, Tsukuba J. Math. 14, 53–69 (1990).
Dung, N. V., Modules with indecomposable decompositions that complement maximal direct summands, J. Algebra 197, 449–467 (1997).
References
Al-attas, A.O. and Vanaja, N., On Σ-extending modules, Comm. Algebra 25, 2365–2393 (1997).
Baba, Y. and Harada, M., On almost M-projectives and almost M-injectives, Tsukuba J. Math. 14, 53–69 (1990).
Jayaraman, M. and Vanaja, N., Harada modules, Comm. Algebra 28, 3703–3726 (2000).
Talebi, Y. and Vanaja, N., Copolyform Σ-lifting modules, Vietnam J. Math. 32, 49–64 (2004).
References
Chang, Ch. and Kuratomi, Y., Lifting modules over right perfect rings, Proc. 36th Symp. Ring Theory and Representation Theory, Yamanashi, 38–41 (2004).
Hanada, K., Kuratomi, Y. and Oshiro, K., On direct sums of extending modules and internal exchange property, Proc. 32nd Symposium on Ring Theory and Representation Theory (Yamaguchi, 1999), 1–17, Tokyo Univ. Agric. Technol., Tokyo (2000).
Kuratomi, Y., On direct sum of lifting modules and internal exchange property, Comm. Algebra 33, 1795–1804 (2005).
Kutami, M. and Oshiro, K., An example of a ring whose projective modules have the exchange property, Osaka J. Math. 17, 415–420 (1980).
Miyashita, Y., Quasi-projective modules, perfect modules, and a theorem for modular lattices, J. Fac. Sci. Hokkaido 19, 86–110 (1966).
Mohamed, S. H., Müller, B. J., and Singh, S., Quasi-dual-continuous modules, J. Aust. Math. Soc., Ser. A 39, 287–299 (1985).
Orhan, N. and Keskin Tütüncü, D., Characterizations of lifting modules in terms of cojective modules and the class of \( \mathcal{B}\left( {\mathcal{M},\mathcal{X}} \right) \) , Int. J. Math. 16(6), 647–660 (2005).
References
Baba, Y. and Harada, M., On almost M-projectives and almost M-injectives, Tsukuba J. Math. 14, 53–69 (1990).
Chamard, J.-Y., Modules quasi-projectifs, projectifs et parfaits, Séminaire Dubreil-Pisot, Algèbre et Théorie des Nombres, 21e année, Nr. 8 (1967/68).
Chang, Ch. and Kuratomi, Y., Lifting modules over right perfect rings, Proc. 36th Symp. Ring Theory and Representation Theory, Yamanashi, 38–41 (2004).
Ganesan, L. and Vanaja, N., Strongly discrete modules, Comm. Algebra, to appear.
Golan, J. S., Quasiperfect modules, Quart. J. Math. Oxford (2), 22, 173–182 (1971).
Harada, M., On modules with lifting properties, Osaka J. Math. 19, 189–201 (1982).
Harada, M. and Mabuchi, T., On almost M-projectives, Osaka J. Math. 26, 837–848 (1989).
Harada, M. and Tozaki, A., Almost M-projectives and Nakayama rings, J. Algebra 122, 447–474 (1989).
Hausen, J. and Johnson, J. A., On supplements in modules, Comm. Math. Univ. Sancti Pauli 37, 29–31 (1982).
Jain, S. K., López-Permouth, S.R. and Tariq Rizvi, S., A characterization of uniserial rings via continuous and discrete modules, J. Aust. Math. Soc., Ser. A 50, 197–203 (1991).
Keskin, D., Supplemented modules and endomorphism rings, PhD Thesis, Hacettepe University, Ankara (1999).
Keskin, D., On lifting modules, Comm. Algebra 28, 3427–3440 (2000).
Keskin, D., Discrete and quasi-discrete modules, Comm. Algebra 30, 5273–5282 (2002).
Kuratomi, Y., On direct sum of lifting modules and internal exchange property, Comm. Algebra 33, 1795–1804 (2005).
Miyashita, Y., Quasi-projective modules, perfect modules, and a theorem for modular lattices, J. Fac. Sci. Hokkaido 19, 86–110 (1966).
Mohamed, S. H. and Müller, B. J., Direct sums of dual continuous modules, Math. Z. 178, 225–232 (1981).
Mohamed, S. H. and Müller, B. J., Continuous and Discrete Modules, London Math. Soc. Lect. Notes Ser. 147, Cambridge Univ. Press, Cambridge (1990).
Mohamed, S. H., Müller, B. J., and Singh, S., Quasi-dual-continuous modules, J. Aust. Math. Soc., Ser. A 39, 287–299 (1985).
Nakahara, S., On a generalization of semiperfect modules, Osaka J. Math. 20, 43–50 (1983).
Oshiro, K., Semiperfect modules and quasi-semiperfect modules, Osaka J. Math. 20, 337–372 (1983).
Oshiro, K., Lifting modules, extending modules and their applications to QF-rings, Hokkaido Math. J. 13, 310–338 (1984).
Oshiro, K., Lifting modules, extending modules and their applications to generalized uniserial rings, Hokkaido Math. J. 13, 339–346 (1984).
Takeuchi, T., On cofinite-dimensional modules, Hokkaido Math. J. 5, 1–43 (1976).
Varadarajan, K., Modules with supplements, Pacific J. Math. 82, 559–564 (1979).
Wisbauer, R., F-semiperfekte und perfekte Moduln in σ[M], Math. Z. 173, 229–234 (1980).
Wisbauer, R., Foundations of Module and Ring Theory, Gordon and Breach, Reading (1991). Grundlagen der Modul-und Ringtheorie, Verlag Reinhard Fischer, München (1988).
Yousif, M. F. and Zhou, Yiqiang, Semiregular, semiperfect and perfect rings relative to an ideal, Rocky Mt. J. Math. 32, 1651–1671 (2002).
Zhou, Yiqiang, Generalizations of perfect, semiperfect and semiregular rings, Algebra Colloq. 7, 305–308 (2000).
Zöschinger, H., Komplemente als direkte Summanden, Arch. Math. 25, 241–253 (1974).
Zöschinger, H., Projektive Moduln mit endlich erzeugtem Radikalfaktormodul, Math. Ann. 255, 199–206 (1981).
References
Byrd, K. A., Some characterization of uniserial ring, Math. Ann. 186, 163–170 (1970).
Colby, R. R. and Rutter, E. A., Jr., Generalization of QF-3 algebras, Trans. Amer. Math. Soc. 153, 371–381 (1971).
Fuller, K. R., Generalized uniserial rings and their Kupisch series, Math. Z. 106, 248–260 (1968).
Khurana, D. and Gupta, R. N., Endomorphism rings of Harada modules, Vietnam J. Math. 28, 173–175 (2000).
Harada, M., On one sided QF-3 rings I, Osaka J. Math. 17, 421–431 (1980).
Harada, M., On one sided QF-3 rings II, Osaka J. Math. 17, 433–438 (1980).
Harada, M., On lifting property on direct sums of hollow modules, Osaka J. Math. 17, 783–791 (1980).
Harada, M., On modules with lifting properties, Osaka J. Math. 19, 189–201 (1982).
Harada, M., Factor categories with applications to direct decomposition of modules, Lect. Notes Pure Appl. Math. 88, Marcel Dekker, New York (1983).
Harada, M. and Mabuchi, T., On almost M-projectives, Osaka J. Math. 26, 837–848 (1989).
Harada, M. and Tozaki, A., Almost M-projectives and Nakayama rings, J. Algebra 122, 447–474 (1989).
Jayaraman, M. and Vanaja, N., Harada modules, Comm. Algebra 28, 3703–3726 (2000).
Kasch, F., Moduln mit LE-Zerlegung und Harada Moduln, Lecture notes, Univ. of Munich (1982).
Kawada, Y., A generalisation of Morita’s theorem concerning generalized uniserial algebras, Proc. Japan Acad. 34, 404–406 (1958).
Oshiro, K., Semiperfect modules and quasi-semiperfect modules, Osaka J. Math. 20, 337–372 (1983).
Oshiro, K., Lifting modules, extending modules and their applications to QF-rings, Hokkaido Math. J. 13, 310–338 (1984).
Oshiro, K., Lifting modules, extending modules and their applications to generalized uniserial rings, Hokkaido Math. J. 13, 339–346 (1984).
Oshiro, K., On Harada rings I, Math. J. Okayama Univ. 31, 161–178 (1989).
Oshiro, K., On Harada rings II, Math. J. Okayama Univ. 31, 179–188 (1989).
Oshiro, K., On Harada rings III, Math. J. Okayama Univ. 32, 111–118 (1990).
Oshiro, K. and Wisbauer, R., Modules with every subgenerated module lifting, Osaka J. Math. 32, 513–519 (1995).
Vanaja, N., Characterization of rings using extending and lifting modules, Ring theory (Granville, OH, 1992), 329–342, World Sci. Publ., River Edge (1993).
References
Abyzov, A. N., Weakly regular modules, Russ. Math. 48(3), 1–3 (2004); transl. from Izv. Vyssh. Uchebn. Zaved. Mat. 2004, No. 3, 3–6.
Baba, Y. and Harada, M., On almost M-projectives and almost M-injectives, Tsukuba J. Math. 14, 53–69 (1990).
Harada, M., On lifting property on direct sums of hollow modules, Osaka J. Math. 17, 783–791 (1980).
Harada, M., On modules with lifting properties, Osaka J. Math. 19, 189–201 (1982).
Harada, M. and Mabuchi, T., On almost M-projectives, Osaka J. Math. 26, 837–848 (1989).
Jayaraman, M. and Vanaja, N., Harada modules, Comm. Algebra 28, 3703–3726 (2000).
Oshiro, K., Lifting modules, extending modules and their applications to QF-rings, Hokkaido Math. J. 13, 310–338 (1984).
Oshiro, K., Lifting modules, extending modules and their applications to generalized uniserial rings, Hokkaido Math. J. 13, 339–346 (1984).
Oshiro, K. and Wisbauer, R., Modules with every subgenerated module lifting, Osaka J. Math. 32, 513–519 (1995).
Vanaja, N., Characterization of rings using extending and lifting modules, Ring theory (Granville, OH, 1992), 329–342, World Sci. Publ., River Edge (1993).
Vanaja, N., All finitely generated M-subgenerated modules are extending, Comm. Algebra 24, 543–572 (1996).
Vanaja, N. and Purav, V. M., Characterisations of generalised uniserial rings in terms of factor rings, Comm. Algebra 20, 2253–2270 (1992).
Vanaja, N. and Purav, V. N., A note on generalised uniserial ring, Comm. Algebra 21, 1153–1159 (1993).
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(2006). From lifting to perfect modules. In: Lifting Modules. Frontiers in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7573-6_5
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