The concept of the strongly π-regular general ring （with or without unity） is introduced and some extensions of strongly π-regular general rings are considered. Two equivalent characterizations on strongly π- reg...The concept of the strongly π-regular general ring （with or without unity） is introduced and some extensions of strongly π-regular general rings are considered. Two equivalent characterizations on strongly π- regular general rings are provided. It is shown that I is strongly π-regular if and only if, for each x ∈I, x^n =x^n＋1y = zx^n＋1 for n ≥ 1 and y, z ∈ I if and only if every element of I is strongly π-regular. It is also proved that every upper triangular matrix general ring over a strongly π-regular general ring is strongly π-regular and the trivial extension of the strongly π-regular general ring is strongly clean.展开更多
In order to study the representation theory of Lie algebras and algebraic groups,Cline,Parshall and Scott put forward the notion of abstract Kazhdan-Lusztig theory for quasi-hereditary algebras.Assume that a quasi-her...In order to study the representation theory of Lie algebras and algebraic groups,Cline,Parshall and Scott put forward the notion of abstract Kazhdan-Lusztig theory for quasi-hereditary algebras.Assume that a quasi-hereditary algebra B has the vertex set Q0 = {1,...,n} such that HomB(P(i),P(j)) = 0 for i > j.In this paper,it is shown that if the quasi-hereditary algebra B has a Kazhdan-Lusztig theory relative to a length function l,then its dual extension algebra A = A(B) has also the Kazhdan-Lusztig theory relative to the length function l.展开更多
基金the Foundation for Excellent Doctoral Dissertation of Southeast University(YBJJ0507)the National Natural Science Foundation of China(10571026)the Natural Science Foundation of Jiangsu Province (Bk2005207).
基金The Foundation for Excellent Doctoral Dissertationof Southeast University (NoYBJJ0507)the National Natural ScienceFoundation of China (No10571026)the Natural Science Foundation ofJiangsu Province (NoBK2005207)
文摘The concept of the strongly π-regular general ring （with or without unity） is introduced and some extensions of strongly π-regular general rings are considered. Two equivalent characterizations on strongly π- regular general rings are provided. It is shown that I is strongly π-regular if and only if, for each x ∈I, x^n =x^n＋1y = zx^n＋1 for n ≥ 1 and y, z ∈ I if and only if every element of I is strongly π-regular. It is also proved that every upper triangular matrix general ring over a strongly π-regular general ring is strongly π-regular and the trivial extension of the strongly π-regular general ring is strongly clean.
基金the Foundation of Zhangzhou Normal University (No.SK05012)
文摘In order to study the representation theory of Lie algebras and algebraic groups,Cline,Parshall and Scott put forward the notion of abstract Kazhdan-Lusztig theory for quasi-hereditary algebras.Assume that a quasi-hereditary algebra B has the vertex set Q0 = {1,...,n} such that HomB(P(i),P(j)) = 0 for i > j.In this paper,it is shown that if the quasi-hereditary algebra B has a Kazhdan-Lusztig theory relative to a length function l,then its dual extension algebra A = A(B) has also the Kazhdan-Lusztig theory relative to the length function l.
