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 this paper,we investigate unitπ regularity and strongly π regularity. We show that every corner ring eRe inherits the unit π regularity from a ring R. We also generalize some important characterizations of abeli...In this paper,we investigate unitπ regularity and strongly π regularity. We show that every corner ring eRe inherits the unit π regularity from a ring R. We also generalize some important characterizations of abelian regular rings to π regular rings and describe strongly π regular rings by virtue of group members.展开更多
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.
文摘In this paper,we investigate unitπ regularity and strongly π regularity. We show that every corner ring eRe inherits the unit π regularity from a ring R. We also generalize some important characterizations of abelian regular rings to π regular rings and describe strongly π regular rings by virtue of group members.
