Yıl 2018, Cilt 22, Sayı 6, Sayfalar 1799 - 1803 2018-12-01

Extending property on EC-Fully Submodules

Ramazan YAŞAR [1] , Adnan TERCAN [2]

54 96

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.

fully invariant, ec-fully submodule, FI-extending, extending, extending
  • [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.
Birincil Dil en
Konular Matematik
Yayımlanma Tarihi December 2018
Dergi Bölümü Araştırma Makalesi
Yazarlar

Yazar: Ramazan YAŞAR (Sorumlu Yazar)
Kurum: HACETTEPE ÜNİVERSİTESİ
Ülke: Turkey


Yazar: Adnan TERCAN

Bibtex @araştırma makalesi { saufenbilder420612, journal = {Sakarya University Journal of Science}, issn = {1301-4048}, eissn = {2147-835X}, address = {Sakarya Üniversitesi}, year = {2018}, volume = {22}, pages = {1799 - 1803}, doi = {10.16984/saufenbilder.420612}, title = {Extending property on EC-Fully Submodules}, key = {cite}, author = {YAŞAR, Ramazan and TERCAN, Adnan} }
APA YAŞAR, R , TERCAN, A . (2018). Extending property on EC-Fully Submodules. Sakarya University Journal of Science, 22 (6), 1799-1803. DOI: 10.16984/saufenbilder.420612
MLA YAŞAR, R , TERCAN, A . "Extending property on EC-Fully Submodules". Sakarya University Journal of Science 22 (2018): 1799-1803 <http://www.saujs.sakarya.edu.tr/issue/31266/420612>
Chicago YAŞAR, R , TERCAN, A . "Extending property on EC-Fully Submodules". Sakarya University Journal of Science 22 (2018): 1799-1803
RIS TY - JOUR T1 - Extending property on EC-Fully Submodules AU - Ramazan YAŞAR , Adnan TERCAN Y1 - 2018 PY - 2018 N1 - doi: 10.16984/saufenbilder.420612 DO - 10.16984/saufenbilder.420612 T2 - Sakarya University Journal of Science JF - Journal JO - JOR SP - 1799 EP - 1803 VL - 22 IS - 6 SN - 1301-4048-2147-835X M3 - doi: 10.16984/saufenbilder.420612 UR - http://dx.doi.org/10.16984/saufenbilder.420612 Y2 - 2018 ER -
EndNote %0 Sakarya University Journal of Science Extending property on EC-Fully Submodules %A Ramazan YAŞAR , Adnan TERCAN %T Extending property on EC-Fully Submodules %D 2018 %J Sakarya University Journal of Science %P 1301-4048-2147-835X %V 22 %N 6 %R doi: 10.16984/saufenbilder.420612 %U 10.16984/saufenbilder.420612
ISNAD YAŞAR, Ramazan , TERCAN, Adnan . "Extending property on EC-Fully Submodules". Sakarya University Journal of Science 22 / 6 (Aralık 2018): 1799-1803. http://dx.doi.org/10.16984/saufenbilder.420612