On Primarily Hollow Module


  • Adil Kadir Jabbar Mathematics Department, College of Science, University of Sulaimani, Kurdistan Region, Iraq. Author
  • Payman Mahmood Hamaali Mathematics Department, College of Science, University of Sulaimani, Kurdistan Region, Iraq. Author




Primary submodule, Primarily hollow module, Multiplication module (submodule)


An R- module  M is called primarily hollow module if every primary submodule of  is a small submodule in. This definition extends several notions in the literature of hollow module. Some certain equivalent conditions to primarily hollow modules. Also, we verified that a primarily hollow module which contains a maximal submodule is a multiplication module and every multiplication primarily hollow module is indecomposable.


El-Bast, Z. A. and Smith, P. P., "Multiplication modules". Communications in Algebra, Vol. 16, No. 4, pp. 755-779. (1988). DOI: https://doi.org/10.1080/00927878808823601

Fleury, P., "Hollow modules and local endomorphism rings". Pacific Journal of Mathematics, Vol. 53, No. 2, pp. 379-385. (1974). DOI: https://doi.org/10.2140/pjm.1974.53.379

Hamaali, P. and Al-Hashimi. B., "Hollow Modules and Semihollow Modules", Journal of Zankoi Sulaimani, Vol. 19. (2017). DOI: https://doi.org/10.17656/jzs.10624

Nikseresht, A. and Sharif, H., "Fully Primary Modules and some Variations". Journal of Algebra and Related Topics, pp. 1-17. (2013).

EL-Atrash, M. S. and Ashour, A. E., "On Primary Compactly Packed Bezout Modules, Department of Mathematics, College of Science, Islamic University of Gaza, Gaza Palestine, pp. 27-28. (2002).

Atani, S. E., Çallıalp, F., and Tekir, Ü. "A short note on the primary submodules of multiplication modules". International Journal of Algebra, Vol. 1, No. 8, pp. 381-384. (2007). DOI: https://doi.org/10.12988/ija.2007.07042

Marcelo, A., Marcelo, F. and Rodríiguez, C., "Some results on prime and primary submodules". Proyecciones (Antofagasta), Vol. 22, No.3, pp. 201-208. (2003). DOI: https://doi.org/10.4067/S0716-09172003000300003

Bataineh, M., and Kuhail, S. "Generalizations of primary ideals and submodules". International Journal of Contemporary Mathematical Sciences, Vol. 6, No. 17-20, pp. 811-824. (2011).

Rangaswamy, K. M. "Modules with finite spanning dimension". Canad. Math. Bull, Vol. 20, No. 2, pp. 255-26. (1977). DOI: https://doi.org/10.4153/CMB-1977-039-4

Tutuncu, D. K., "On Coclosed Submodules", Indian J. Pure appl. Math, Vol. 36, No. 3, pp. 135-144. (2005).

Bland, P. E. "Rings and their modules". Walter de Gruyter. (2011). DOI: https://doi.org/10.1515/9783110250237

Ware, R., "Endomorphism rings of projective modules". Transactions of the American Mathematical Society, Vol. 155, No. 1, pp. 233-256. (1971). DOI: https://doi.org/10.1090/S0002-9947-1971-0274511-2

Azizi, A., and Jayaram, C., "Some applications of the product of submodules in multiplication modules". Iranian Journal of Science and Technology (Sciences), Vol. 35, No. 4, pp. 273-277. (2011).

Ebrahimpour, M., On generalisations of almost prime and weakly prime ideals. Bulletin of the Iranian Mathematical Society, Vol. 40, No. 2, pp. 531-540. (2014).

Ebrahimpour, M., and Nekooei, R., "On Generalization of prime submodules". Bulletin of the Iranian Mathematical Society, Vol. 39, No. 5, pp. 919-939. (2013).

Varadarajan, K., "Dual Goldie dimension", Comm. Algebra, Vol. 7, No. 6, pp. 565–610. (1979). DOI: https://doi.org/10.1080/00927877908822364

Reiter, E., "A dual to the Goldie ascending chain condition on direct sums of submodules", Bull. Calcutta Math. Soc., Vol. 73, pp. 55–63. (1981).

Grezeszcuk, P. and Puczylowski, E., "On Goldie and dual Goldie dimension", Journal of Pure and Applied Algebra, Vol. 31, pp. 47–55. (1984). DOI: https://doi.org/10.1016/0022-4049(84)90075-6

Zhao, R., "Uniform and couniform dimension of generalized inverse polynomial modules". Bulletin of the Korean Mathematical Society, Vol. 49, No. 5, pp. 1067-1079. (2012). DOI: https://doi.org/10.4134/BKMS.2012.49.5.1067



How to Cite

On Primarily Hollow Module. (2018). Journal of Zankoy Sulaimani - Part A, 20(3-4), 95-104. https://doi.org/10.17656/jzs.10738

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