BOUNDED MATRICES OVER REGULAR RINGS

Title & Authors
BOUNDED MATRICES OVER REGULAR RINGS
Wang Shuqin; Chen Huanyin;

Abstract
In this paper, we investigate bounded matrices over regular rings. We observe that every bounded matrix over a regular ring can be described by idempotent matrices and invertible matrices. Let A, $\small{B{in}M_n(R)}$ be bounded matrices over a regular ring R. We prove that $(AB)^d Keywords bounded matrix;idempotent matrix;invertible matrix; Language English Cited by References 1. P. Ara, Strongly$\pi$-regular rings have stable range one, Proc. Amer. Math. Soc. 124 (1996), no. 11, 3293-3298 2. P. Ara, K. R. Goodearl, K. C. O'Meara, and E. Pardo, Diagonalization of ma- trices over regular rings, Linear Algebra Appl. 265 (1997), 147-163 3. M. J. Canfell, Completion of diagrams by automorphisms and Bass' first stable range condition, J. Algebra 176 (1995), no. 2, 480-503 4. J. J. Carmona, J. Cuf and P. Menal, On the unit 1-stable rank of rings of analytic functions, Publ. Mat. 36 (1992), no. 2A, 439-447 5. H. Chen, Exchange rings with Artinian primitive factors, Algebr. Represent. Theory 2 (1999), no. 2, 201-207 6. H. Chen, Units, idempotents, and stable range conditions, Comm. Algebra 29 (2001), no. 2, 703-717 7. H. Chen, Exchange rings having stable range one, Int. J. Math. Math. Sci. 25 (2001), no. 12, 763-770 8. H. Chen, Extensions of rings with many units, Comm. Algebra 31 (2003), no. 5, 2403-2416 9. K. R. Goodearl, von Neumann regular rings, Pitman, London, San Francisco, Melbourne, 1979 10. K. R. Goodearl, von Neumann regular rings, second ed., Krieger, Malabar, Fl., 1991 11. M. Henriksen, On a class of regular rings that are elementary divisor rings, Arch. Math.(Basel) 24 (1973), 133-141 12. P. Menal and J. Moncasi, Lifting units in self-injective rings and an index theory for Rickart C$^{\ast}\$-algebras, Pacific J. Math. 126 (1987), no. 2, 295-329

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