We provide several characterizations and investigate properties of Prüfer modules. In fact, we study the connections of such modules with their endomorphism rings. We also prove that for any Prüfer module M, the forcing linearity number of M, fln(M), belongs to {0,1}.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1201, author = {S. Ebrahimi Atani and S. Dolati Pishhesari and M. Khoramdel}, title = {Some remarks on Pr\"ufer modules}, journal = {Discussiones Mathematicae - General Algebra and Applications}, volume = {33}, year = {2013}, pages = {121-128}, zbl = {1328.13013}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1201} }
S. Ebrahimi Atani; S. Dolati Pishhesari; M. Khoramdel. Some remarks on Prüfer modules. Discussiones Mathematicae - General Algebra and Applications, Tome 33 (2013) pp. 121-128. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1201/
[000] [1] M. Alkan, B. Saraç and Y. Tiraş, Dedekind Modules, Comm. Alg. 33(5) (2005) 1617-1626. doi: 10.1081/AGB-200061007.
[001] [2] D.D. Anderson and D.F. Anderson, Cancellation modules and related modules, in: Lect. Notes Pure Appl. Math, 220 (Ed(s)), (Dekker, New York, 2001) 13-25. | Zbl 1037.13005
[002] [3] Z.A. El-Bast and P.F. Smith, Multiplication modules, Comm. Alg. 16(4) (1988) 755-779. doi: 10.1080/00927878808823601. | Zbl 0642.13002
[003] [4] J. Hausen and J.A. Johnson, Centralizer near-rings that are rings, J. Austral. Soc. (Series A) 59 (1995) 173-183. doi: 10.1017/S144678870003857X. | Zbl 0852.16032
[004] [5] I. Kaplansky, Commutative Rings (Boston: Allyn and Bacon, 1970). | Zbl 0203.34601
[005] [6] M. Khoramdel and S. Dolati Pish Hesari, Some notes on Dedekind modules, Hacettepe Journal of Mathematics and Statistics 40(5) (2011) 627-634.
[006] [7] H. Matsumura, Commutative Ring Theory (Cambridge: Cambridge University Press, 1989). doi: 10.1017/CBO9781139171762.
[007] [8] C.J. Maxson and J.H. Meyer, Forcing linearity numbers, J. Algebra 223 (2000) 190-207. doi: 10.1006/jabr.1999.7991. | Zbl 0953.16034
[008] [9] A.G. Naoum and F.H. Al-Alwan, Dedekind modules, Comm. Alg. 24(2) (1996) 397-412. doi: 10.1080/00927879608825576. | Zbl 0858.13008
[009] [10] A.G. Naoum, On the ring of endomorphisms of finitely generated multiplication modules, Period. Math. Hungar. 21(3) (1990) 249-255. doi: 10.1007/BF02651092. | Zbl 0739.13004
[010] [11] A.Ç. Özcan, A. Harmanci and P.F. Smith, Duo modules, Glasg. Math. J. 48 (2006) 533-545. doi: 10.1017/S0017089506003260. | Zbl 1116.16003
[011] [12] J.J. Rotman, An Introduction to Homological Algebra (Academic Press, New York, 1979). | Zbl 0441.18018
[012] [13] B. Saraç, P.F. Smith and Y. Tiraş, On Dedekind Modules, Comm. Alg. 35(5) (2007) 1533-1538. doi: 10.1080/00927870601169051. | Zbl 1113.13011
[013] [14] J. Sanwong, Forcing Linearity Numbers for Multiplication Modules, Comm. Alg. 34 (2006) 4591-4596. doi: 10.1080/00927870600936740. | Zbl 1120.16006
[014] [15] P.F. Smith, Multiplication Modules and Projective Modules, Period. Math. Hungar. 29(2) (1994) 163-168. doi: 10.1007/BF01876873. | Zbl 0824.13008