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ON ω-LOCAL MODULES AND Rad-SUPPLEMENTED MODULES
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 Title & Authors
ON ω-LOCAL MODULES AND Rad-SUPPLEMENTED MODULES
Buyukasik, Engin; Tribak, Rachid;
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 Abstract
All modules considered in this note are over associative commutative rings with an identity element. We show that a -local module M is Rad-supplemented if and only if M/P(M) is a local module, where P(M) is the sum of all radical submodules of M. We prove that -local nonsmall submodules of a cyclic Rad-supplemented module are again Rad-supplemented. It is shown that commutative Noetherian rings over which every w-local Rad-supplemented module is supplemented are Artinian. We also prove that if a finitely generated Rad-supplemented module is cyclic or multiplication, then it is amply Rad-supplemented. We conclude the paper with a characterization of finitely generated amply Rad-supplemented left modules over any ring (not necessarily commutative).
 Keywords
-local modules;Rad-supplemented modules;amply Rad-supplemented modules;
 Language
English
 Cited by
1.
RAD-SUPPLEMENTING MODULES, Journal of the Korean Mathematical Society, 2016, 53, 2, 403  crossref(new windwow)
 References
1.
R. Ameri, On the prime submodules of multiplication modules, Int. J. Math. Math. Sci. 2003 (2003), no. 27, 1715-1724. crossref(new window)

2.
F.W. Anderson and K. R. Fuller, Rings and Categories of Modules, New-York, Springer-Verlag, 1974.

3.
E. Buyukasik and C. Lomp, On a recent generalization of semiperfect rings, Bull. Aust. Math. Soc. 78 (2008), no. 2, 317-325. crossref(new window)

4.
E. Buyukasik, E. Mermut, and S. Ozdemir, Rad-supplemented modules, Rend. Semin. Mat. Univ. Padova 124 (2010), 157-177. crossref(new window)

5.
J. Clark, C. Lomp, N. Vanaja, and R. Wisbauer, Lifting Modules, Supplements and Projectivity in Module Theory. Basel: Frontiers in Mathematics, Birkhauser Verlag, 2006.

6.
S. Ecevit, M. T. Kosan, and R. Tribak. Rad-${\oplus}$-supplemented modules and cofinitely Rad-${\oplus}$-supplemented modules, Algebra Colloq. 19 (2012), no. 4, 637-648. crossref(new window)

7.
A. I. Generalov, The w-cohigh purity in a category of modules, Math. Notes 33 (1983), 402-408; translation from Mat. Zametki 33 (1983), no. 5, 785-796. crossref(new window)

8.
V. N. Gerasimov and I. I. Sakhaev. A counterexample to two conjectures on projective and flat modules, Sibirsk. Mat. Zh. 25 (1984), no. 6, 31-35. crossref(new window)

9.
R. W. Gilmer, Multiplicative Ideal Theory, New York, Marcel Dekker, 1972.

10.
R. M. Hamsher, Commutative Noetherian rings over which every module has a maximal submodule, Proc. Amer. Math. Soc. 17 (1966), 1471-1472.

11.
S. H. Mohamed and B. J. Muller, Continuous and Discrete Modules, Cambridge, UK: London Math. Soc. Lecture Note Ser 147, Cambridge University Press, 1990.

12.
P. Rudlof, On the structure of couniform and complemented modules, J. Pure Appl. Algebra 74 (1991), no. 3, 281-305. crossref(new window)

13.
P. Rudlof, On minimax and related modules, Canad. J. Math. 44 (1992), no. 1, 154-166. crossref(new window)

14.
P. F. Smith, Finitely generated supplemented modules are amply supplemented, Arab. J. Sci. Eng. Sect. C Theme Issues 25 (2000), no. 2, 69-79.

15.
R. Tribak, On ${\delta}$-local modules and amply ${\delta}$-supplemented modules, J. Algebra Appl. 12 (2013), no. 2, 1250144, 14 pages.

16.
E. Turkmen and A. Pancar, On cofinitely Rad-supplemented modules, Int. J. Pure Appl. Math. 53 (2009), no. 2, 153-162.

17.
Y.Wang and N. Ding, Generalized supplemented modules, Taiwanese J. Math. 10 (2006), no. 6, 1589-1601.

18.
R. Ware, Endomorphism rings of projective modules, Trans. Amer. Math. Soc. 155 (1971), no. 1, 233-256. crossref(new window)

19.
R. Wisbauer, Foundations of Module and Ring Theory, Philadelphia: Gordon and Breach Science Publishers, 1991.

20.
H. Zoschinger, Gelfandringe und koabgeschlossene Untermoduln, Bayer. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. 3 (1982), 43-70.

21.
H. Zoschinger, Minimax-moduln, J. Algebra 102 (1986), no. 1, 1-32. crossref(new window)