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Year 2018, Volume: 22 Issue: 6, 1799 - 1803, 01.12.2018
https://doi.org/10.16984/saufenbilder.420612

Abstract

References

  • [1] Birkenmeier, G. F., Müller, B. J. and Rizvi S. T., “Modules in which every fully invariant submodule is Essential in a Direct Summand,” Communications in Algebra, vol. 30, no.3, pp. 1395-1415, 2007. [2] Birkenmeier, G. F., Park, J. K. and Rizvi, S. T., Extensions of rings and modules, New York: Birkhäuser, 2013.[3] Celep, C. and Tercan A., "Modules whose ec-closed submodules are direct summand," Taiwanese Journal of Mathematics, vol.13, no.4, pp. 1247-1256, 2009.[4] Dung, N. V., Huynh, D. V., Smith, P. F., and Wisbauer, R., Extending Modules, Pitman Research Notes in Mathematics Series, 313, Longmon, New York, 1994.[5] Kamal, M. A., and Elmnophy, O. A., "On P-extending modules," Acta Math. Univ. Comenianae, vol. 74, no. 2, pp. 279-286, 2005.[6] Kara, Y., Tercan, A. and Yaşar R., "PI-extending modules via nontrivial complex bundles and Abelian endomorphism rings," Bulletin of the Iranian Mathematical Society, vol. 43, no. 1, pp. 121-129, 2017.[7] Lam, T.Y., Lectures on modules and rings, vol. 189. Springer Science and Business Media, 2012.[8] Smith, P. F., and Tercan, A., "Direct summands of modules which satisfy (C-11)," Algebra Colloquium, vol. 11, pp. 231-237, 2004.[9] Smith, P. F., and Tercan, A., “Generalizations of CS-modules,” Communications in Algebra, vol. 21, no.6, pp.1809-1847, 1993.[10] Tercan, A. and Yücel, C. C., Module theory, extending modules and generalizations, Basel: Birkhäuser, 2016.

Extending property on EC-Fully Submodules

Year 2018, Volume: 22 Issue: 6, 1799 - 1803, 01.12.2018
https://doi.org/10.16984/saufenbilder.420612

Abstract

There
are several generalizations of -modules
in literature. One of the generalization is based on fully invariant
submodules. Recall that a
module  is called -extending
if every fully invariant submodule is essential in a direct summand. We call a module
-extending
if every fully invariant submodule which contains essentially a cyclic
submodule is essential in a direct summand. Initially we obtain basic
properties in the general module setting. For example, a direct sum of -extending
modules is -extending.
Again, like the -extending
property, the -extending
property is shown to carry over to matrix rings.

References

  • [1] Birkenmeier, G. F., Müller, B. J. and Rizvi S. T., “Modules in which every fully invariant submodule is Essential in a Direct Summand,” Communications in Algebra, vol. 30, no.3, pp. 1395-1415, 2007. [2] Birkenmeier, G. F., Park, J. K. and Rizvi, S. T., Extensions of rings and modules, New York: Birkhäuser, 2013.[3] Celep, C. and Tercan A., "Modules whose ec-closed submodules are direct summand," Taiwanese Journal of Mathematics, vol.13, no.4, pp. 1247-1256, 2009.[4] Dung, N. V., Huynh, D. V., Smith, P. F., and Wisbauer, R., Extending Modules, Pitman Research Notes in Mathematics Series, 313, Longmon, New York, 1994.[5] Kamal, M. A., and Elmnophy, O. A., "On P-extending modules," Acta Math. Univ. Comenianae, vol. 74, no. 2, pp. 279-286, 2005.[6] Kara, Y., Tercan, A. and Yaşar R., "PI-extending modules via nontrivial complex bundles and Abelian endomorphism rings," Bulletin of the Iranian Mathematical Society, vol. 43, no. 1, pp. 121-129, 2017.[7] Lam, T.Y., Lectures on modules and rings, vol. 189. Springer Science and Business Media, 2012.[8] Smith, P. F., and Tercan, A., "Direct summands of modules which satisfy (C-11)," Algebra Colloquium, vol. 11, pp. 231-237, 2004.[9] Smith, P. F., and Tercan, A., “Generalizations of CS-modules,” Communications in Algebra, vol. 21, no.6, pp.1809-1847, 1993.[10] Tercan, A. and Yücel, C. C., Module theory, extending modules and generalizations, Basel: Birkhäuser, 2016.
There are 1 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Ramazan Yaşar

Adnan Tercan

Publication Date December 1, 2018
Submission Date May 3, 2018
Acceptance Date June 26, 2018
Published in Issue Year 2018 Volume: 22 Issue: 6

Cite

APA Yaşar, R., & Tercan, A. (2018). Extending property on EC-Fully Submodules. Sakarya University Journal of Science, 22(6), 1799-1803. https://doi.org/10.16984/saufenbilder.420612
AMA Yaşar R, Tercan A. Extending property on EC-Fully Submodules. SAUJS. December 2018;22(6):1799-1803. doi:10.16984/saufenbilder.420612
Chicago Yaşar, Ramazan, and Adnan Tercan. “Extending Property on EC-Fully Submodules”. Sakarya University Journal of Science 22, no. 6 (December 2018): 1799-1803. https://doi.org/10.16984/saufenbilder.420612.
EndNote Yaşar R, Tercan A (December 1, 2018) Extending property on EC-Fully Submodules. Sakarya University Journal of Science 22 6 1799–1803.
IEEE R. Yaşar and A. Tercan, “Extending property on EC-Fully Submodules”, SAUJS, vol. 22, no. 6, pp. 1799–1803, 2018, doi: 10.16984/saufenbilder.420612.
ISNAD Yaşar, Ramazan - Tercan, Adnan. “Extending Property on EC-Fully Submodules”. Sakarya University Journal of Science 22/6 (December 2018), 1799-1803. https://doi.org/10.16984/saufenbilder.420612.
JAMA Yaşar R, Tercan A. Extending property on EC-Fully Submodules. SAUJS. 2018;22:1799–1803.
MLA Yaşar, Ramazan and Adnan Tercan. “Extending Property on EC-Fully Submodules”. Sakarya University Journal of Science, vol. 22, no. 6, 2018, pp. 1799-03, doi:10.16984/saufenbilder.420612.
Vancouver Yaşar R, Tercan A. Extending property on EC-Fully Submodules. SAUJS. 2018;22(6):1799-803.