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

journal contribution

posted on 2023-05-16, 11:13 authored by Kelarev, AV, van der Merwe, B, van Wyk, LWe prove that the minimum number v = v(Script U signm(R)) such that the m Ã— 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)) = âŒˆlog2 mâŒ‰ for every m â‰¥ 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). Â© 1998 Academic Press.

## History

## Publication title

Journal of Algebra## Volume

205## Pagination

605-616## ISSN

0021-8693## Department/School

School of Natural Sciences## Publisher

Academic Press## Place of publication

U.S.A.## Repository Status

- Restricted