Rad-supplemented modules
Engin Büyükaşik; Engin Mermut; Salahattin Özdemir
Rendiconti del Seminario Matematico della Università di Padova (2010)
- Volume: 124, page 157-177
- ISSN: 0041-8994
Access Full Article
topHow to cite
topBüyükaşik, Engin, Mermut, Engin, and Özdemir, Salahattin. "Rad-supplemented modules." Rendiconti del Seminario Matematico della Università di Padova 124 (2010): 157-177. <http://eudml.org/doc/243435>.
@article{Büyükaşik2010,
author = {Büyükaşik, Engin, Mermut, Engin, Özdemir, Salahattin},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {supplements; coneat modules; supplement submodules; proper classes; supplemented modules; Dedekind domains},
language = {eng},
pages = {157-177},
publisher = {Seminario Matematico of the University of Padua},
title = {Rad-supplemented modules},
url = {http://eudml.org/doc/243435},
volume = {124},
year = {2010},
}
TY - JOUR
AU - Büyükaşik, Engin
AU - Mermut, Engin
AU - Özdemir, Salahattin
TI - Rad-supplemented modules
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2010
PB - Seminario Matematico of the University of Padua
VL - 124
SP - 157
EP - 177
LA - eng
KW - supplements; coneat modules; supplement submodules; proper classes; supplemented modules; Dedekind domains
UR - http://eudml.org/doc/243435
ER -
References
top- [1] K. Al-Takhman - C. Lomp - R. Wisbauer, -complemented and -supplemented modules, Algebra Discrete Math., 3 (2006), pp. 1--16. Zbl1116.16005MR2321929
- [2] R. Alizade - G. Bilhan - P. F. Smith, Modules whose maximal submodules have supplements, Comm. Algebra, 29 (6) (2001), pp. 2389--2405. Zbl0989.16001MR1845118
- [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. Zbl0301.16001MR1245487
- [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. Zbl0854.16014MR1344221
- [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. Zbl0483.16026MR655412
- [7] P. E. Bland, Topics in torsion theory, volume 103 of Mathematical Research, Wiley-VCH Verlag Berlin GmbH, Berlin, 1998. Zbl0899.16013MR1640903
- [8] D. Buchsbaum, A note on homology in categories, Ann. of Math., 69 (1) (1959), pp. 66--74. Zbl0084.26801MR140556
- [9] E. Büyükaşik - C. Lomp, On a recent generalization of semiperfect rings, Bull. Aust. Math. Soc., 78 (2) (2008), pp. 317--325. Zbl1159.16015MR2466867
- [10] J. Clark - C. Lomp - N. Vanaja - R. Wisbauer, Lifting modules, Frontiers in Mathematics. Birkhäuser Verlag, Basel, 2006. Supplements and projectivity in module theory. Zbl1102.16001MR2253001
- [11] L. Fuchs, Infinite Abelian Groups, volume 1. Academic Press, New York, 1970. Zbl0209.05503
- [12] A. I. Generalov, The -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. Zbl0521.16022MR706232
- [13] J. S. Golan, Torsion theories, volume 29 of Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman Scientific & Technical, Harlow, 1986. Zbl0657.16017MR880019
- [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. Zbl0127.25402MR156882
- [15] K. Honda, Realism in the theory of abelian groups I, Comment. Math. Univ. St. Paul, 5 (1956), pp. 37--75. Zbl0071.02404MR80093
- [16] I. Kaplansky, Modules over Dedekind rings and valuation rings, Trans. Amer. Math. Soc., 72 (1952), pp. 327--340. Zbl0046.25701MR46349
- [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. Zbl0523.16001MR667346
- [18] T. Y. Lam, A first course in noncommutative rings, volume 131 of Graduate Texts in Mathematics, Springer-Verlag, New York, second edition, 2001. Zbl0980.16001MR1838439
- [19] C. Lomp, On semilocal modules and rings, Comm. Algebra, 27 (4) (1999), pp. 1921--1935. Zbl0927.16012MR1679679
- [20] S. Maclane, Homology. Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963. Zbl0328.18009MR156879
- [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). Zbl0224.13015MR276212
- [23] S. Nakahara, On a generalization of semiperfect rings, Osaka J. Math., 20 (1) (1983), pp. 43--50. Zbl0513.16020MR695616
- [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. Zbl0449.16028MR498703
- [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. Zbl0296.16001MR389953
- [27] Bo T. Stenström, High submodules and purity, Arkiv för Matematik, 7 (11) (1967), pp. 173--176. Zbl0153.34303MR223353
- [28] Bo T. Stenström, Pure submodules, Arkiv för Matematik, 7 (10) (1967), pp. 159--171. Zbl0153.34302MR223425
- [29] Y. Wang - N. Ding, Generalized supplemented modules, Taiwanese J. Math., 10 (6) (2006), pp. 1589--1601. Zbl1122.16003MR2275148
- [30] R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Reading, 1991. Zbl0746.16001MR1144522
- [31] W. Xue, Characterization of semiperfect and perfect rings, Publicacions Matematiques, 40 (1) (1996), pp. 115--125. Zbl0863.16014MR1397010
- [32] H. Zöschinger, Komplementierte Moduln über Dedekindringen, J. Algebra, 29 (1974), pp. 42--56. Zbl0277.13008MR340347
- [33] H. Zöschinger, Koatomare Moduln, Math. Z., 170 (3) (1980), pp. 221--232. Zbl0411.13009MR564202
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.