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Some remarks on Prüfer modules

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Języki publikacji
EN
Abstrakty
EN
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}.
Twórcy
  • Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914 Rasht, Iran
  • Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914 Rasht, Iran
autor
  • Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914 Rasht, Iran
Bibliografia
  • [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.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1201
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