Noncommutative Curves of Genus Zero
Related to Finite Dimensional Algebras
2009
American Mathematical Society (Verlag)
978-0-8218-4400-7 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-4400-7 (ISBN)
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Investigates noncommutative smooth projective curves of genus zero, also called exceptional curves. This title shows that each such curve X admits, up to some weighting, a projective coordinate algebra which is a not necessarily commutative graded factorial domain R in the sense of Chatters and Jordan.
In these notes the author investigates noncommutative smooth projective curves of genus zero, also called exceptional curves. As a main result he shows that each such curve X admits, up to some weighting, a projective coordinate algebra which is a not necessarily commutative graded factorial domain R in the sense of Chatters and Jordan. Moreover, there is a natural bijection between the points of X and the homogeneous prime ideals of height one in R, and these prime ideals are principal in a strong sense.
In these notes the author investigates noncommutative smooth projective curves of genus zero, also called exceptional curves. As a main result he shows that each such curve X admits, up to some weighting, a projective coordinate algebra which is a not necessarily commutative graded factorial domain R in the sense of Chatters and Jordan. Moreover, there is a natural bijection between the points of X and the homogeneous prime ideals of height one in R, and these prime ideals are principal in a strong sense.
| Erscheint lt. Verlag | 30.9.2009 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Zusatzinfo | illustrations |
| Verlagsort | Providence |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 0-8218-4400-8 / 0821844008 |
| ISBN-13 | 978-0-8218-4400-7 / 9780821844007 |
| Zustand | Neuware |
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