We solve two problems about ascent sequences： how to get the ascent sequence of the reflection of A with respect to its antidiagonal for a matrix A ∈ Intn and its ascent sequences, and how to determine the ascent se...We solve two problems about ascent sequences： how to get the ascent sequence of the reflection of A with respect to its antidiagonal for a matrix A ∈ Intn and its ascent sequences, and how to determine the ascent sequence of A＋B for kxk matrices A ∈ Int, and B ∈ Intm. We give the other definition of ascent se- quence and get M-sequence. For the first question, we define M-sequence of A and rewrite the ascent sequences as another form We build the bijection between M-sequences and ascent sequences and prove that our bijection is well-defined. For the second ques- tion, we define an operation on M-sequences. On the basis of the operation and the bijections, we get the ascent sequences of the sum of two matrices.展开更多
A ring is said to be right （resp., left） regular-duo if every right （resp., left） regular element is regular. The structure of one-sided regular elements is studied in various kinds of rings, especially, upper tri...A ring is said to be right （resp., left） regular-duo if every right （resp., left） regular element is regular. The structure of one-sided regular elements is studied in various kinds of rings, especially, upper triangular matrix rings over one-sided Ore domains. We study the structure of （one-sided） regular-duo rings, and the relations between one-sided regular-duo rings and related ring theoretic properties.展开更多
基金Supported by the National Natural Science Foundation of China(61262088,61063042)the Natural Science Foundation Project of Xinjiang Uygur Autonomous Region(2011211A011)
文摘We solve two problems about ascent sequences： how to get the ascent sequence of the reflection of A with respect to its antidiagonal for a matrix A ∈ Intn and its ascent sequences, and how to determine the ascent sequence of A＋B for kxk matrices A ∈ Int, and B ∈ Intm. We give the other definition of ascent se- quence and get M-sequence. For the first question, we define M-sequence of A and rewrite the ascent sequences as another form We build the bijection between M-sequences and ascent sequences and prove that our bijection is well-defined. For the second ques- tion, we define an operation on M-sequences. On the basis of the operation and the bijections, we get the ascent sequences of the sum of two matrices.
文摘A ring is said to be right （resp., left） regular-duo if every right （resp., left） regular element is regular. The structure of one-sided regular elements is studied in various kinds of rings, especially, upper triangular matrix rings over one-sided Ore domains. We study the structure of （one-sided） regular-duo rings, and the relations between one-sided regular-duo rings and related ring theoretic properties.
