Goldie absolute direct summand rings and modules
DOI:
https://doi.org/10.24193/subbmath.2018.4.02Keywords:
Goldie extending modules, ADS modules, CS modules.Abstract
In the present paper, we introduce and study Goldie ADS modules and rings, which subsume two generalizations of Goldie extending modules due to Akalan et al. [3] and ADS-modules due to Alahmadi et al. [7]. A module M will be called a Goldie ADS module if for every decomposition M = S ⊕ T of M and every complement T l of S, there exists a submodule D of M such that T lβD and M = S ⊕ D. Various properties concerning direct sums of Goldie ADS modules are established. Mathematics Subject Classification (2010): 16D40, 16E50, 16N20.References
Abdioglu, C., Zemlicka, J., On type-ADS modules and rings, Journal of Algebra and Its Applications, https://doi.org/10.1142/S0219498818500834.
Agayev, N., Leghwel, A., Ko¸san, M.T., Harmanci, A., Duo modules and duo rings, Far East J. Math. Sci, 20(2005), no. 3, 341-346.
Akalan, E., Birkenmeier, G.F, Tercan, A., Goldie extending modules , Commun. Algebra, 37(2009), no. 3, 663-683.
Akalan, E., Birkenmeier, G.F., Tercan, A., Corrigendum to: Goldie extending modules, Commun. Algebra, 38(2010), 4747-4748.
Akalan, E., Birkenmeier, G.F., Tercan, A., Goldie extending rings, Comm. Algebra, 40(2012), no. 3, 423-428.
Akalan, E., Birkenmeier, G.F., Tercan, A., Corrigendum to: Goldie extending modules, Commun. Algebra, 41(2013), no. 4, 2005-2005.
Alahmadi, A., Jain, S.K., Leroy, A., ADS modules, J. Algebra, 352(2012), 215-222.
Amin, I., Yousif, M., Zeyada, N., Soc-Injective Rings and Modules, Comm. Algebra, 33(11)(2005), 4229-4250.
Dung, N.V., Huynh, D.V., Smith, P.F., Wisbauer, R., Extending modules, Pitman Research Notes in Math. Longman, 1994, 313.
Fuchs, L., Infinite Abelian Groups, vol. I, Pure Appl. Math. Ser. Monogr. Textb. vol. 36, Academic Press, New York, San Francisco, London 1970.
Kuratomi, Y., Goldie extending modules and generalizations of quasi-continuous modules, Tsukuba J. Math, 38(2014), no. 1, 25-37.
Mohammed, S.H., Mu¨ller, B.J., Continous and Discrete Modules, London Math. Soc. LN. Cambridge Univ. Press, 1990, 147.
Nicholson, W.K., Yousif, M.F., Quasi-Frobenius Rings, Cambridge Univ. Press, 2003. [14] Quynh, T.C., Ko¸san, M.T., On ADS modules, Commun. Algebra, 42(2014), 3541-3551.
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