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The Minimum Number of Idempotent Generators of a Complete Blocked Triangular Matrix Algebra

โœ Scribed by A.B. van der Merwe; L. van Wyk

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
119 KB
Volume
222
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

Let R be a complete blocked triangular matrix algebra over an infinite field F. Assume that R is not an upper triangular matrix algebra or a full matrix algebra.

ลฝ . We prove that the minimum number s R such that R can be generated as an F-algebra by idempotents, is given by

where m is the number of 1 = 1 diagonal blocks of R. We also show that R can 1 be generated as an F-algebra by two elements, and if m s 0, R can be generated 1 by an idempotent and a nilpotent element.

๐Ÿ“œ SIMILAR VOLUMES

The Minimum Number of Idempotent Generat
The Minimum Number of Idempotent Generators of an Upper Triangular Matrix Algebra
โœ A.V Kelarev; A.B van der Merwe; L van Wyk ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 161 KB

In order to prove the result mentioned above, we show that R s log m 2 for every m G 2, where R ลฝ m. denotes the direct sum of m copies of R. The ลฝ . latter result corrects an error by N.

On the Number of Blocks in a Generalized
On the Number of Blocks in a Generalized Steiner System
โœ J.H van Lint ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 208 KB

We consider t-designs with \*=1 (generalized Steiner systems) for which the block size is not necessarily constant. An inequality for the number of blocks is derived. For t=2, this inequality is the well known De Bruijn Erdo s inequality. For t>2 it has the same order of magnitude as the Wilson Petr