DECOMPOSING LINEAR TRANSFORMATIONS

作者：Wang Lu; Zhou Yiqiang^*

来源：Bulletin of the Australian Mathematical Society, 2011, 83(2): 256-261.

DOI：10.1017/S0004972710001711

• linear transformation
• unit
• unit 1-stable range

Let R be the ring of linear transformations of a right vector space over a division ring D. Three results are proved: (1) if vertical bar D vertical bar > 4, then for any a E R there exists a unit u of R such that a + u, a u and a u(-1) are units of R; (2) if vertical bar D vertical bar > 3, then for any a E R there exists a unit u of R such that both a + u and a u units of R; (3) if I DI > 2, then for any a is an element of R there exists a unit u of R such that both a u and a u I are units of R. The second result extends the main result in H. Chen, ['Decompositions of countable linear transformations', Glasg. Math. J. (2010), doi:10.1017/S0017089510000121] and the third gives an affirmative answer to the question raised in the same paper.

• 出版日期2011-4