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 introduce a concept,called Σ-associated primes,that is a generalization of both associated primes and nilpotent associated primes.We first observe the basic properties of Σ-associated primes and con...In this paper we introduce a concept,called Σ-associated primes,that is a generalization of both associated primes and nilpotent associated primes.We first observe the basic properties of Σ-associated primes and construct typical examples.We next describe all Σ-associated primes of the Ore extension R[x; α,δ],the skew Laurent polynomial ring R[x,x-1; α] and the skew power series ring R[[x; α]],in terms of the Σ-associated primes of R in a very straightforward way.Consequently several known results relating to associated primes and nilpotent associated primes are extended to a more general setting.展开更多
An associative ring with identity R is called Armendariz if, whenever （∑^m i=0^aix^i）（∑^n j=0^bjx^j）=0 in R[x],aibj=0 for all i and j. An associative ring with identity is called reduced if it has no non-zero ni...An associative ring with identity R is called Armendariz if, whenever （∑^m i=0^aix^i）（∑^n j=0^bjx^j）=0 in R[x],aibj=0 for all i and j. An associative ring with identity is called reduced if it has no non-zero nilpotent elements. In this paper, we define a general reduced ring （with or without identity） and a general Armendariz ring （with or without identity）, and identify a class of maximal general Armendariz subrings of matrix rings over general reduced rings.展开更多
China is using military hotlines as a way to build mutual military trust with other countries Telephones have been a convenient and efficient means of communicat- ing since they were invented in the late 19th century....China is using military hotlines as a way to build mutual military trust with other countries Telephones have been a convenient and efficient means of communicat- ing since they were invented in the late 19th century.Today,governments use military hotlines for instant access to top-level military leaders in other countries in times of crisis.But they also believe hot- lines can be used to promote greater com- munication with and a better understanding of other military leaders.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.
基金Supported by the National Natural Science Foundation of China(Grant No.11071062)the Scientific Research Fundation of Hunan Provincial Education Department(Grant No.12B101)
文摘In this paper we introduce a concept,called Σ-associated primes,that is a generalization of both associated primes and nilpotent associated primes.We first observe the basic properties of Σ-associated primes and construct typical examples.We next describe all Σ-associated primes of the Ore extension R[x; α,δ],the skew Laurent polynomial ring R[x,x-1; α] and the skew power series ring R[[x; α]],in terms of the Σ-associated primes of R in a very straightforward way.Consequently several known results relating to associated primes and nilpotent associated primes are extended to a more general setting.
文摘An associative ring with identity R is called Armendariz if, whenever （∑^m i=0^aix^i）（∑^n j=0^bjx^j）=0 in R[x],aibj=0 for all i and j. An associative ring with identity is called reduced if it has no non-zero nilpotent elements. In this paper, we define a general reduced ring （with or without identity） and a general Armendariz ring （with or without identity）, and identify a class of maximal general Armendariz subrings of matrix rings over general reduced rings.
文摘China is using military hotlines as a way to build mutual military trust with other countries Telephones have been a convenient and efficient means of communicat- ing since they were invented in the late 19th century.Today,governments use military hotlines for instant access to top-level military leaders in other countries in times of crisis.But they also believe hot- lines can be used to promote greater com- munication with and a better understanding of other military leaders.
