### Citations

176 |
Noncommutative projective schemes
- Artin, Zhang
- 1994
(Show Context)
Citation Context ...graded ring from certain data. The resultant graded ring is called the twisted homogeneous coordinate ring and plays an important role in noncommutative projective geometry and representation theory (=-=[1, 2, 4, 5, 6]-=-). This construction is similar to the procedure to take the tensor algebra TA(σ) over a ring A of an A−A bi-module σ equipped with the grading deg σ := 1. In some case twisted homogeneous coordinate ... |

21 | n-representation-finite algebras and n-APR tilting
- Iyama, Oppermann
(Show Context)
Citation Context ...y of path algebras of quivers. Actually they introduced the notion of n-hereditary algebra and proved the dichotomy that an n-hereditary algebra is either n-representation finite (which is defined in =-=[3]-=-) or n-representation infinite. Moreover they studied the representation theory of n-representation infinite algebras and introduced the notions of n-preprojective, n-preinjective and n-regular module... |

10 |
Noncommutative proj and coherent
- Polishchuk
(Show Context)
Citation Context ...graded ring from certain data. The resultant graded ring is called the twisted homogeneous coordinate ring and plays an important role in noncommutative projective geometry and representation theory (=-=[1, 2, 4, 5, 6]-=-). This construction is similar to the procedure to take the tensor algebra TA(σ) over a ring A of an A−A bi-module σ equipped with the grading deg σ := 1. In some case twisted homogeneous coordinate ... |

8 | The structure of AS-Gorenstein algebras,
- Minamoto, Mori
- 2011
(Show Context)
Citation Context ...graded ring from certain data. The resultant graded ring is called the twisted homogeneous coordinate ring and plays an important role in noncommutative projective geometry and representation theory (=-=[1, 2, 4, 5, 6]-=-). This construction is similar to the procedure to take the tensor algebra TA(σ) over a ring A of an A−A bi-module σ equipped with the grading deg σ := 1. In some case twisted homogeneous coordinate ... |

2 |
n-representation infinite algebras, arXiv:1205.1272
- Herschend, Iyama, et al.
(Show Context)
Citation Context |

2 |
Ampleness of two-sided tilting complexes, Int
- Minamoto
(Show Context)
Citation Context |

1 |
Note des membres et correspondats et note présentées ou transmises par leurs soins
- Soublin
- 1968
(Show Context)
Citation Context ...gain right Noetherian. Contrary to this, it is well-known for specialists that even if a ring A is right coherent, the polynomial ring A[t] in one variable could fail to be coherent. In fact, Soublin =-=[7]-=- showed that the ring A = Q[[x, y]]ΠN has such a property. In this note we show that if we take gradings into account, then the polynomial ring A[X ] become graded coherent for any coherent ring A. Na... |