In this paper,from the Anick’s resolution and Grobner-Shirshov basis for quantized enveloping algebra of type C_(3),we compute the minimal projective resolution of the trivial module U_(q)+(C_(3))and as an applicatio...In this paper,from the Anick’s resolution and Grobner-Shirshov basis for quantized enveloping algebra of type C_(3),we compute the minimal projective resolution of the trivial module U_(q)+(C_(3))and as an application,we obtain that the global dimension of U_(q)+(C_(3))is 9.展开更多
The correlation between the resolution for a Zariskian filtered ring R and that for its associated graded ring G(R) is discussed in this note. Then we show some examples satisfying the condition of the theorem.
Let Λ and Γ be left and right Noetherian rings and Λ U a generalized tilting module with Γ = End( Λ U ). For a non-negative integer k, if Λ U is (k - 2)-Gorenstein with the injective dimensions of Λ U and U Γ ...Let Λ and Γ be left and right Noetherian rings and Λ U a generalized tilting module with Γ = End( Λ U ). For a non-negative integer k, if Λ U is (k - 2)-Gorenstein with the injective dimensions of Λ U and U Γ being k, then the socle of the last term in a minimal injective resolution of Λ U is non-zero.展开更多
Abstract. We find the minimal free resolution of a fat star-configuration X in Pn of type （r, s,t） defined by general forms of degrees d1,...,dr, and show that a fat linear star- configuration X in P2 never has gene...Abstract. We find the minimal free resolution of a fat star-configuration X in Pn of type （r, s,t） defined by general forms of degrees d1,...,dr, and show that a fat linear star- configuration X in P2 never has generic Hilbert function if （s,t） ≠ （1, 1） or （2, 2）. These two results generalize the interesting results of [2].展开更多
In this paper,by using the Anick resolution and Grobner-Shirshov basis for quantized enveloping algebra of type B2,we compute the minimal projective resolution of the trivial module of Uq^+(B2),and as an application w...In this paper,by using the Anick resolution and Grobner-Shirshov basis for quantized enveloping algebra of type B2,we compute the minimal projective resolution of the trivial module of Uq^+(B2),and as an application we compute the global dimension of Uq^+(B2).展开更多
Abstract In this paper, by using the Anick＇s resolution and Grobner-Shirshov basis for quantized enveloping algebra of type G2, we compute the minimal projective resolution of the trivial module of Uq＋ （G2） and as...Abstract In this paper, by using the Anick＇s resolution and Grobner-Shirshov basis for quantized enveloping algebra of type G2, we compute the minimal projective resolution of the trivial module of Uq＋ （G2） and as an application we compute the global dimension of Uq＋（G2）.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11971384)the Natural Science Foundation of Shaanxi Province(Grant No.2021JQ-894)。
文摘In this paper,from the Anick’s resolution and Grobner-Shirshov basis for quantized enveloping algebra of type C_(3),we compute the minimal projective resolution of the trivial module U_(q)+(C_(3))and as an application,we obtain that the global dimension of U_(q)+(C_(3))is 9.
基金Project supported by NNSF of China and NSF of Beijing
文摘The correlation between the resolution for a Zariskian filtered ring R and that for its associated graded ring G(R) is discussed in this note. Then we show some examples satisfying the condition of the theorem.
基金supported by the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20060284002)National Natural Science Foundation of China (Grant No. 10771095)Natural Science Foundation of Jiangsu Province of China (Grant No. BK2007517)
文摘Let Λ and Γ be left and right Noetherian rings and Λ U a generalized tilting module with Γ = End( Λ U ). For a non-negative integer k, if Λ U is (k - 2)-Gorenstein with the injective dimensions of Λ U and U Γ being k, then the socle of the last term in a minimal injective resolution of Λ U is non-zero.
文摘Abstract. We find the minimal free resolution of a fat star-configuration X in Pn of type （r, s,t） defined by general forms of degrees d1,...,dr, and show that a fat linear star- configuration X in P2 never has generic Hilbert function if （s,t） ≠ （1, 1） or （2, 2）. These two results generalize the interesting results of [2].
文摘In this paper,by using the Anick resolution and Grobner-Shirshov basis for quantized enveloping algebra of type B2,we compute the minimal projective resolution of the trivial module of Uq^+(B2),and as an application we compute the global dimension of Uq^+(B2).
基金Supported by National Natural Science Puondation of China(Grant No.11361056)
文摘Abstract In this paper, by using the Anick＇s resolution and Grobner-Shirshov basis for quantized enveloping algebra of type G2, we compute the minimal projective resolution of the trivial module of Uq＋ （G2） and as an application we compute the global dimension of Uq＋（G2）.
