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On SIP and SSP Modules

Year 2018, Volume: 6 Issue: 2, 124 - 128, 01.06.2018

Fatih Karabacak

Abstract

M has the summmand intersection property (SIP), if the intersection of every two direct summands in M is a direct summand in M, and a module has the summand sum property (SSP), if the sum of every two direct summand in M is a direct summand in M. In this note, we show that modules have these properties under some conditions.

Keywords

Direct summand SIP-modules

References

  • [1] Anderson FW, Fuller KR. Rings and Categories of modules. New York, USA: Springer-Verlag, 1974
  • [2] Fuchs L. Infinite Abelian Groups. Academic Press, New York, USA:1970.
  • [3] Kaplansky I. Infinite Abelian Groups. Michigan, USA: university of Michigan, 1969.
  • [4] Wilson GV. Modules with on the direct summand intersection proerty. Comm. Algebra 1986; 14: 21-38.
  • [5] Garcia JL. Properties of direct summands of modules. Comm. Algebra 1989; 17(1): 73-92.
  • [6] Alkan M, Harmancı A. On summand sum and summand intersection property of modules. Turk J. Math 2002; 26:131-147.
  • [7] Dung NV, Huyn DV, Smith PF, Wisbauer R. Extending Modules, London, UK: Longman, 1990.
  • [8] Clark J, Lomp C, Vanaja N, Wisbauer R. Lifting Modules. Berlin, Germany: Birkhause Verlag, 2006.
  • [9] Azarpanah F. Sum and intersection of summand ideals in C(X). Comm Algebra1999; 27:5548-5560.
  • [10] Smith PF. Fully invariant multiplication modules. Palest. J. Math 2015; 4(1): 462-470.
  • [11] Akalan E, Birkenmeier GF, Tercan A. Goldie extending modules. Comm. Algebra 2009; 37:663-683.
  • [12] Takıl Mutlu F. On ADS-modules with the SIP. Bull. Iranian Soc. 2015; 41:1355-1363.
  • [13]Quyn TC, Koşan MT. On ADS modules and rings. Comm Algebra. 2014; 42:3541-3551.
  • [14] Karabacak F, Tercan A. On modules and matrix rings with SIP-extending. Taiwanese J. Math. 2007; 11(4): 1037-1044.

Year 2018, Volume: 6 Issue: 2, 124 - 128, 01.06.2018

Fatih Karabacak

Abstract

References

  • [1] Anderson FW, Fuller KR. Rings and Categories of modules. New York, USA: Springer-Verlag, 1974
  • [2] Fuchs L. Infinite Abelian Groups. Academic Press, New York, USA:1970.
  • [3] Kaplansky I. Infinite Abelian Groups. Michigan, USA: university of Michigan, 1969.
  • [4] Wilson GV. Modules with on the direct summand intersection proerty. Comm. Algebra 1986; 14: 21-38.
  • [5] Garcia JL. Properties of direct summands of modules. Comm. Algebra 1989; 17(1): 73-92.
  • [6] Alkan M, Harmancı A. On summand sum and summand intersection property of modules. Turk J. Math 2002; 26:131-147.
  • [7] Dung NV, Huyn DV, Smith PF, Wisbauer R. Extending Modules, London, UK: Longman, 1990.
  • [8] Clark J, Lomp C, Vanaja N, Wisbauer R. Lifting Modules. Berlin, Germany: Birkhause Verlag, 2006.
  • [9] Azarpanah F. Sum and intersection of summand ideals in C(X). Comm Algebra1999; 27:5548-5560.
  • [10] Smith PF. Fully invariant multiplication modules. Palest. J. Math 2015; 4(1): 462-470.
  • [11] Akalan E, Birkenmeier GF, Tercan A. Goldie extending modules. Comm. Algebra 2009; 37:663-683.
  • [12] Takıl Mutlu F. On ADS-modules with the SIP. Bull. Iranian Soc. 2015; 41:1355-1363.
  • [13]Quyn TC, Koşan MT. On ADS modules and rings. Comm Algebra. 2014; 42:3541-3551.
  • [14] Karabacak F, Tercan A. On modules and matrix rings with SIP-extending. Taiwanese J. Math. 2007; 11(4): 1037-1044.
There are 14 citations in total.

Details

Journal Section Articles
Authors

Fatih Karabacak This is me

Publication Date June 1, 2018
Published in Issue Year 2018 Volume: 6 Issue: 2

Cite

APA Karabacak, F. (2018). On SIP and SSP Modules. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler, 6(2), 124-128.
AMA Karabacak F. On SIP and SSP Modules. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler. June 2018;6(2):124-128.
Chicago Karabacak, Fatih. “On SIP and SSP Modules”. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler 6, no. 2 (June 2018): 124-28.
EndNote Karabacak F (June 1, 2018) On SIP and SSP Modules. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler 6 2 124–128.
IEEE F. Karabacak, “On SIP and SSP Modules”, Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler, vol. 6, no. 2, pp. 124–128, 2018.
ISNAD Karabacak, Fatih. “On SIP and SSP Modules”. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler 6/2 (June 2018), 124-128.
JAMA Karabacak F. On SIP and SSP Modules. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler. 2018;6:124–128.
MLA Karabacak, Fatih. “On SIP and SSP Modules”. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler, vol. 6, no. 2, 2018, pp. 124-8.
Vancouver Karabacak F. On SIP and SSP Modules. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler. 2018;6(2):124-8.