Rank and decomposition of infinite matrix over a division ring are discussed. Two rank-finite matrices are same-inverse equivalent if and only if their rank equal is proved.
讨论除环上无限方阵的秩及分解问题。证明了除环上秩有限的二无限方阵同逆等价的充要条件是它们的秩相等。
2
We generalize the rank ofmatrices over a division ring to the B-rank ofmatrices over a ring with identity and study properties for the B-rank ofmatrices over a ring with identity.
我们将体上矩阵的秩推广为含幺环上矩阵的B-秩，并研究了含幺环上矩阵的B—秩的性质。
3
The number of the elementary matrices representing a matrix over a local ring are discussed, the corresponding results from a field to a local ring are extended.