Some remarks on Prüfer modules
Discussiones Mathematicae. General Algebra and Applications, Tome 33 (2013) no. 2, pp. 121-128.

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: Prüfer modules, Prüfer domains, invertible submodules, duo modules, forcing linearity number
@article{DMGAA_2013_33_2_a0,
     author = {Atani, S. and Pishhesari, S. and Khoramdel, M.},
     title = {Some remarks on {Pr\"ufer} modules},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {121--128},
     publisher = {mathdoc},
     volume = {33},
     number = {2},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2013_33_2_a0/}
}
TY  - JOUR
AU  - Atani, S.
AU  - Pishhesari, S.
AU  - Khoramdel, M.
TI  - Some remarks on Prüfer modules
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2013
SP  - 121
EP  - 128
VL  - 33
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2013_33_2_a0/
LA  - en
ID  - DMGAA_2013_33_2_a0
ER  - 
%0 Journal Article
%A Atani, S.
%A Pishhesari, S.
%A Khoramdel, M.
%T Some remarks on Prüfer modules
%J Discussiones Mathematicae. General Algebra and Applications
%D 2013
%P 121-128
%V 33
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2013_33_2_a0/
%G en
%F DMGAA_2013_33_2_a0
Atani, S.; Pishhesari, S.; Khoramdel, M. Some remarks on Prüfer modules. Discussiones Mathematicae. General Algebra and Applications, Tome 33 (2013) no. 2, pp. 121-128. http://geodesic.mathdoc.fr/item/DMGAA_2013_33_2_a0/

[1] M. Alkan, B. Saraç and Y. Tiraş, Dedekind Modules, Comm. Alg. 33(5) (2005) 1617-1626. doi: 10.1081/AGB-200061007.

[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.

[3] Z.A. El-Bast and P.F. Smith, Multiplication modules, Comm. Alg. 16(4) (1988) 755-779. doi: 10.1080/00927878808823601.

[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.

[5] I. Kaplansky, Commutative Rings (Boston: Allyn and Bacon, 1970).

[6] M. Khoramdel and S. Dolati Pish Hesari, Some notes on Dedekind modules, Hacettepe Journal of Mathematics and Statistics 40(5) (2011) 627-634.

[7] H. Matsumura, Commutative Ring Theory (Cambridge: Cambridge University Press, 1989). doi: 10.1017/CBO9781139171762.

[8] C.J. Maxson and J.H. Meyer, Forcing linearity numbers, J. Algebra 223 (2000) 190-207. doi: 10.1006/jabr.1999.7991.

[9] A.G. Naoum and F.H. Al-Alwan, Dedekind modules, Comm. Alg. 24(2) (1996) 397-412. doi: 10.1080/00927879608825576.

[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.

[11] A.Ç. Özcan, A. Harmanci and P.F. Smith, Duo modules, Glasg. Math. J. 48 (2006) 533-545. doi: 10.1017/S0017089506003260.

[12] J.J. Rotman, An Introduction to Homological Algebra (Academic Press, New York, 1979).

[13] B. Saraç, P.F. Smith and Y. Tiraş, On Dedekind Modules, Comm. Alg. 35(5) (2007) 1533-1538. doi: 10.1080/00927870601169051.

[14] J. Sanwong, Forcing Linearity Numbers for Multiplication Modules, Comm. Alg. 34 (2006) 4591-4596. doi: 10.1080/00927870600936740.

[15] P.F. Smith, Multiplication Modules and Projective Modules, Period. Math. Hungar. 29(2) (1994) 163-168. doi: 10.1007/BF01876873.