Öz
Kaynakça
- P. Holgate, Groupoids Satisfying a Simple Invertive Law, The Mathematics Student 61(1-4) (1992) 101-106.
- M. A. Kazim, M. Naseeruddin, On Almost Semigroups, Alig. Bull. Math. 2 (1972) 1-7.
- Q. Mushtaq, S. M. Yusuf, On LA-Semigroups, Alig. Bull. Math. 8(1978) 65-70.
- J. R. Cho, J. Jezek, T. Kepka, Paramedial Groupoids, Czechoslovak Mathematical Journal 49(2) (1999) 277-290.
- Q. Mushtaq, M. S. Kamran, On Left Almost Groups, Proceedings of the Pakistan Academy of Sciences 33(1996) 1-2.
- Q. Mushtaq, Zeroids and Idempoids in AG-Groupoids, Quasigroups and Related Systems 11(2004).
- Q. Mushtaq, M. Khan, Direct Product of Abel Grassmann's Groupoids, Journal of Interdisciplinary Mathematics 11 (2008) 461-467.
- M. Shah, T. Shah, A. Ali, On The Cancellativity of AG-Groupoids, International Mathematical Forum 6(44) (2011) 2187-2194.
Öz
An Abel-Grassmann's groupoid (brie
y AG-groupoid) is a groupoid S satisfying the left invertive law: (xy)z = (zy)x for all x, y, z \in S. In the present paper, we
discuss the left and right cancellative property of elements of the nite AG-groupoid S. For an AG-groupoid with left identity it is known that every left cancellative ele-
ment is right cancellative. We prove a problem (for nite AG-groupoids) that every left cancellative element of an AG-groupoid (without left identity) is right cancella-
tive. Moreover, we generalize various results of nite AG-groupoids by removing the condition of existence of left identity.
Anahtar Kelimeler
AG-groupoid AG-subgroupoid Cancellative elements non-cancellative elements
Kaynakça
- P. Holgate, Groupoids Satisfying a Simple Invertive Law, The Mathematics Student 61(1-4) (1992) 101-106.
- M. A. Kazim, M. Naseeruddin, On Almost Semigroups, Alig. Bull. Math. 2 (1972) 1-7.
- Q. Mushtaq, S. M. Yusuf, On LA-Semigroups, Alig. Bull. Math. 8(1978) 65-70.
- J. R. Cho, J. Jezek, T. Kepka, Paramedial Groupoids, Czechoslovak Mathematical Journal 49(2) (1999) 277-290.
- Q. Mushtaq, M. S. Kamran, On Left Almost Groups, Proceedings of the Pakistan Academy of Sciences 33(1996) 1-2.
- Q. Mushtaq, Zeroids and Idempoids in AG-Groupoids, Quasigroups and Related Systems 11(2004).
- Q. Mushtaq, M. Khan, Direct Product of Abel Grassmann's Groupoids, Journal of Interdisciplinary Mathematics 11 (2008) 461-467.
- M. Shah, T. Shah, A. Ali, On The Cancellativity of AG-Groupoids, International Mathematical Forum 6(44) (2011) 2187-2194.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 26 Mart 2020 |
| Gönderilme Tarihi | 21 Şubat 2019 |
| Yayımlandığı Sayı | Yıl 2020 Sayı: 30 |
Kaynak Göster
- Makale Dosyaları