Öz
In this note we deal with the internal cancellation property for free modules. To this end we deduce that the internal cancellation property is not Morita invariant. In contrast, it is shown that the direct sum of two copies of a right Ore domain has the internal cancellation property as a right module over itself
Anahtar Kelimeler
Internal Cancellation Property; Matrix Rings; Tangent Bundle of a Sphere; Ads-Module.
Kaynakça
- Bhatwadekar, S.M. (2003). A cancellation for projective modules over affine algebras over C-fields. 1 J. Pure and App. Algebra 183, 17-26.
- Bredon, G.E. (1993). Topology and Geometry. Springer Verlag, New York.
- Brookfield, G. (1998). Direct Sum Cancellation of Noetherian Modules. J. Algebra 200, 207-224.
- Burgess, W.D. and Raphael, R. (1992). On modules with The Absolute Direct Summand Property. Proceedings of the Ohio State University Conference, 137-148.
- Khurana, D. and Lam, T.Y. (2005). Rings with Internal Cancellation. J. Algebra 284, 203-235.
- Lam, T.Y. (1999). Lectures on Modules and Rings. Springer Verlag, New York.
- Mohamed, S.H. and Muller, B.J. (1990). Continuous and Discrete Modules. Cambridge University Press.
- Ojanguren, M. and Sridharan, R. (1971). Cancellation of Azumaya Algebras. J. Algebra 18, 501-505.
- Smith, P.F. and Tercan, A. (1992). Continuous and quasi-continuous modules. Houston J. Math. 18, 339-348.
- Swan, R. G. (1962). Vector bundles and projective modules. Trans. Amer. Math. Soc. 105, 264-277.
- Swan, R. G. (1996). Quaternionic Bundles on Algebraic Spheres. Rocky Mountain J. Math. 262, 773- 791.
Öz
Bu çalışmada serbest modüller için iç kısaltma özelliği incelenmiştir. Sonuç olarak, iç kısaltma
özelliğinin Morita değişmez olmadığı sonucuna varılmıştır. Tersine, bir sağ Ore Bölgesinin kendisi ile
dik toplamının, kendi üzerine bir sağ modül olarak, iç kısaltma özelliğine sahip olduğu gösterilmiştir.
Anahtar Kelimeler
İç kısaltma özelliği Matris halkaları Bir kürenin teğet demeti Ads-Modül
Kaynakça
- Bhatwadekar, S.M. (2003). A cancellation for projective modules over affine algebras over C-fields. 1 J. Pure and App. Algebra 183, 17-26.
- Bredon, G.E. (1993). Topology and Geometry. Springer Verlag, New York.
- Brookfield, G. (1998). Direct Sum Cancellation of Noetherian Modules. J. Algebra 200, 207-224.
- Burgess, W.D. and Raphael, R. (1992). On modules with The Absolute Direct Summand Property. Proceedings of the Ohio State University Conference, 137-148.
- Khurana, D. and Lam, T.Y. (2005). Rings with Internal Cancellation. J. Algebra 284, 203-235.
- Lam, T.Y. (1999). Lectures on Modules and Rings. Springer Verlag, New York.
- Mohamed, S.H. and Muller, B.J. (1990). Continuous and Discrete Modules. Cambridge University Press.
- Ojanguren, M. and Sridharan, R. (1971). Cancellation of Azumaya Algebras. J. Algebra 18, 501-505.
- Smith, P.F. and Tercan, A. (1992). Continuous and quasi-continuous modules. Houston J. Math. 18, 339-348.
- Swan, R. G. (1962). Vector bundles and projective modules. Trans. Amer. Math. Soc. 105, 264-277.
- Swan, R. G. (1996). Quaternionic Bundles on Algebraic Spheres. Rocky Mountain J. Math. 262, 773- 791.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Yazarlar | |
| Yayımlanma Tarihi | 17 Ağustos 2011 |
| IZ | https://izlik.org/JA63GU63TU |
| Yayımlandığı Sayı | Yıl 2011 Cilt: 1 Sayı: 2 |