Rad-supplemented modules

Büyükaşik, Engin ; Mermut, Engin ; Özdemir, Salahattin

Rendiconti del Seminario Matematico della Università di Padova, Tome 124 (2010), p. 157-177 / Harvested from Numdam

Détail

Publié le : 2010-01-01

MR 2752682 | Zbl 1246.16007

Bibliographie

[1] K. Al-Takhman - C. Lomp - R. Wisbauer, ${\tau } $-complemented and ${\tau } $-supplemented modules, Algebra Discrete Math., 3 (2006), pp. 1--16. | MR 2321929 | Zbl 1116.16005

[2] R. Alizade - G. Bilhan - P. F. Smith, Modules whose maximal submodules have supplements, Comm. Algebra, 29 (6) (2001), pp. 2389--2405. | MR 1845118 | Zbl 0989.16001

[3] R. Alizade - E. Mermut, The inductive closure of supplements, Journal of the Faculty of Science Ege University, 27 (2004), pp. 33--48.

[4] F. W. Anderson - K. R. Fuller, Rings and Categories of Modules, Springer, New-York, 1992. | MR 1245487 | Zbl 0301.16001

[5] G. Azumaya, A characterization of semi-perfect rings and modules, In "Ring Theory," Proc. Biennial Ohio-Denison Conf., World Scientific Publ. (Singapore, 1992) pp. 28--40. | MR 1344221 | Zbl 0854.16014

[6] L. Bican - T. Kepka - P. Němec, Rings, modules, and preradicals, volume 75 of Lecture Notes in Pure and Applied Mathematics, Marcel Dekker Inc., New York, 1982. | MR 655412 | Zbl 0483.16026

[7] P. E. Bland, Topics in torsion theory, volume 103 of Mathematical Research, Wiley-VCH Verlag Berlin GmbH, Berlin, 1998. | MR 1640903 | Zbl 0899.16013

[8] D. Buchsbaum, A note on homology in categories, Ann. of Math., 69 (1) (1959), pp. 66--74. | MR 140556 | Zbl 0084.26801

[9] E. Büyükaşik - C. Lomp, On a recent generalization of semiperfect rings, Bull. Aust. Math. Soc., 78 (2) (2008), pp. 317--325. | MR 2466867 | Zbl 1159.16015

[10] J. Clark - C. Lomp - N. Vanaja - R. Wisbauer, Lifting modules, Frontiers in Mathematics. Birkhäuser Verlag, Basel, 2006. Supplements and projectivity in module theory. | MR 2253001 | Zbl 1102.16001

[11] L. Fuchs, Infinite Abelian Groups, volume 1. Academic Press, New York, 1970.

[12] A. I. Generalov, The $w$-cohigh purity in a category of modules, Math. Notes, 33 (5-6) (1983), pp. 402--408. Translated from Russian from Mat. Zametki, 33 (5) (1983), pp. 785--796. | MR 706232 | Zbl 0521.16022

[13] J. S. Golan, Torsion theories, volume 29 of Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman Scientific & Technical, Harlow, 1986. | MR 880019 | Zbl 0657.16017

[14] D. K. Harrison - J. M. Irwin - C. L. Peercy - E. A. Walker, High extensions of abelian groups, Acta Math. Acad. Sci. Hunger., 14 (1963), pp. 319--330. | MR 156882 | Zbl 0127.25402

[15] K. Honda, Realism in the theory of abelian groups I, Comment. Math. Univ. St. Paul, 5 (1956), pp. 37--75. | MR 80093 | Zbl 0071.02404

[16] I. Kaplansky, Modules over Dedekind rings and valuation rings, Trans. Amer. Math. Soc., 72 (1952), pp. 327--340. | MR 46349 | Zbl 0046.25701

[17] F. Kasch, Modules and rings, volume 17 of London Mathematical Society Monographs. Academic Press Inc. [Harcourt Brace Jovanovich Publishers], London, 1982. Translated from the German and with a preface by D. A. R. Wallace. | MR 667346 | Zbl 0523.16001

[18] T. Y. Lam, A first course in noncommutative rings, volume 131 of Graduate Texts in Mathematics, Springer-Verlag, New York, second edition, 2001. | MR 1838439 | Zbl 0980.16001

[19] C. Lomp, On semilocal modules and rings, Comm. Algebra, 27 (4) (1999), pp. 1921--1935. | MR 1679679 | Zbl 0927.16012

[20] S. Maclane, Homology. Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963. | MR 156879 | Zbl 0328.18009

[21] E. Mermut, Homological Approach to Complements and Supplements, PhD thesis, Dokuz Eylül University, The Graduate School of Natural and Applied Sciences, İzmir/Turkey, 2004. http://www.fbe.deu.edu.tr/ALL_FILES/Tez_Arsivi/2004/DR-t403.pdf.

[22] A. P. Mishina - L. A. Skornyakov, Abelian groups and modules, volume 107 of American Mathematical Society Translations. Ser. 2. American Mathematical Society, Providence, R. I., 1976. Translated from Russian from Abelevy gruppy i moduli, Izdat. Nauka, Moscow (1969). | MR 276212

[23] S. Nakahara, On a generalization of semiperfect rings, Osaka J. Math., 20 (1) (1983), pp. 43--50. | MR 695616 | Zbl 0513.16020

[24] S. Özdemir, Neat and coneat subgroups, M. Sc. Thesis, Dokuz Eylül University, The Graduate School of Natural and Applied Sciences, İzmir/Turkey, 2007. http://www.fbe.deu.edu.tr/ALL_FILES/Tez_Arsivi/2007/YL_t2256.pdf.

[25] E. G. Sklyarenko, Relative homological algebra in categories of modules, Russian Math. Surveys, 33 (3) (1978), pp. 97--137. Traslated from Russian from Uspehi Mat. Nauk, 33, no. 3 (201), (1978), pp. 85--120. | MR 498703 | Zbl 0449.16028

[26] Bo T. Stenström, Rings of quotients, Springer-Verlag, New York, 1975. Die Grundlehren der Mathematischen Wissenschaften, Band 217, An introduction to methods of ring theory. | MR 389953 | Zbl 0296.16001

[27] Bo T. Stenström, High submodules and purity, Arkiv för Matematik, 7 (11) (1967), pp. 173--176. | MR 223353 | Zbl 0153.34303

[28] Bo T. Stenström, Pure submodules, Arkiv för Matematik, 7 (10) (1967), pp. 159--171. | MR 223425 | Zbl 0153.34302

[29] Y. Wang - N. Ding, Generalized supplemented modules, Taiwanese J. Math., 10 (6) (2006), pp. 1589--1601. | MR 2275148 | Zbl 1122.16003

[30] R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Reading, 1991. | MR 1144522 | Zbl 0746.16001

[31] W. Xue, Characterization of semiperfect and perfect rings, Publicacions Matematiques, 40 (1) (1996), pp. 115--125. | MR 1397010 | Zbl 0863.16014

[32] H. Zöschinger, Komplementierte Moduln über Dedekindringen, J. Algebra, 29 (1974), pp. 42--56. | MR 340347 | Zbl 0277.13008

[33] H. Zöschinger, Koatomare Moduln, Math. Z., 170 (3) (1980), pp. 221--232. | MR 564202 | Zbl 0411.13009