Abstract
In this study, the modules whose p-submodules have a complement which is a direct summand are explored. The module theoretical properties such as direct sums and summands are investigated. As opposed to direct sums, this condition does not transfer to the direct summands. Thus, it is examined that under what conditions the direct summands fulfill the property. Examples are given to demonstrate the results.
References
- Dung, N. V., Huynh, D. V., Smith, P. F., Wisbauer, R., Extending Modules, Longman, Harlow, (1994).
- Birkenmeier, G. F., Tercan, A., Yücel, C. C., The extending condition relative to sets of submodules, Communications in Algebra 42, 764-778, (2014).
- Kaplansky, I., Infinite Abelian Groups, University of Michigan Press, (1969).
- Smith, P. F., Tercan A., Generalizations of CS-modules, Communications in Algebra 21(6), 1809-1847, (1993).
- Tercan, A., On CLS-modules, Rocky Mountain Journal of Mathematics, 25(4), 1557-1564, (1995).
- Tercan, A., Yücel, C. C., Module Theory, Extending Modules and Generalizations, Birkhäuser, Basel, (2016).
- Fuchs, L,. Infinite Abelian Groups I, Academic Press, New York, (1970).
- Kara, Y., Modules whose p -submodules are direct summands, Turkish Journal of Mathematics, 42 (1), 28-33, (2018).
- Goodearl, K. R., Ring Theory: Nonsingular Rings and Modules, Dekker, New York, (1976).
- Garcia, J. L., Properties of direct summands of modules, Communications in Algebra, 17(1), 73–92, (1989).
Abstract
Bu çalışmada p-alt modüllerinin tümleyeni dik toplanan olan modüller araştırılmıştır. Dik toplam ve dik toplanan gibi modül teorik özellikler incelenmiştir. Dik toplamın aksine, bu modül özelliği dik toplananlara taşınmadığından, hangi koşullar altında ilgili özelliğin dik toplananlara aktarıldığı üzerinde çalışılmıştır. Elde edilen sonuçları niteleyen örneklere yer verilmiştir.
References
- Dung, N. V., Huynh, D. V., Smith, P. F., Wisbauer, R., Extending Modules, Longman, Harlow, (1994).
- Birkenmeier, G. F., Tercan, A., Yücel, C. C., The extending condition relative to sets of submodules, Communications in Algebra 42, 764-778, (2014).
- Kaplansky, I., Infinite Abelian Groups, University of Michigan Press, (1969).
- Smith, P. F., Tercan A., Generalizations of CS-modules, Communications in Algebra 21(6), 1809-1847, (1993).
- Tercan, A., On CLS-modules, Rocky Mountain Journal of Mathematics, 25(4), 1557-1564, (1995).
- Tercan, A., Yücel, C. C., Module Theory, Extending Modules and Generalizations, Birkhäuser, Basel, (2016).
- Fuchs, L,. Infinite Abelian Groups I, Academic Press, New York, (1970).
- Kara, Y., Modules whose p -submodules are direct summands, Turkish Journal of Mathematics, 42 (1), 28-33, (2018).
- Goodearl, K. R., Ring Theory: Nonsingular Rings and Modules, Dekker, New York, (1976).
- Garcia, J. L., Properties of direct summands of modules, Communications in Algebra, 17(1), 73–92, (1989).
Details
| Primary Language | English |
|---|---|
| Journal Section | Research Articles |
| Authors | |
| Publication Date | July 4, 2021 |
| Submission Date | March 10, 2021 |
| Published in Issue | Year 2021 Volume: 23 Issue: 2 |