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The minimum number of idempotent generators of an upper triangular matrix algebra

Citation

Kelarev, AV and van der Merwe, B and van Wyk, L, The minimum number of idempotent generators of an upper triangular matrix algebra, Journal of Algebra, 205, (2) pp. 605-616. ISSN 0021-8693 (1998) [Refereed Article]

DOI: doi:10.1006/jabr.1997.7405

Abstract

We prove that the minimum number v = v(Script U signm(R)) such that the m × m upper triangular matrix algebra Script U signm(R) over an arbitrary commutative ring R can be generated as an R-algebra by v idempotents, is given by (formula presented) In order to prove the result mentioned above, we show that v(R(m)) = ⌈log2 m⌉ for every m ≥ 2, where R(m) denotes the direct sum of m copies of R. The latter result corrects an error by N. Krupnik (Comm. Algebra 20, 1992, 3251-3257). © 1998 Academic Press.

Item Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Pure Mathematics
Research Field:Algebra and Number Theory
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Kelarev, AV (Dr Andrei Kelarev)
ID Code:14015
Year Published:1998
Web of Science® Times Cited:2
Deposited By:Mathematics
Deposited On:1998-08-01
Last Modified:2011-08-09
Downloads:0

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