Notes on Whitehead space of an algebra

M. Arian-Nejad

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 31, 1-4

Abstract:

Let R be a ring, and denote by [ R , R ] the group generated additively by the additive commutators of R . When R n = M n ( R ) (the ring of n × n matrices over R ), it is shown that [ R n , R n ] is the kernel of the regular trace function modulo [ R , R ] . Then considering R as a simple left Artinian F -central algebra which is algebraic over F with Char   F = 0 , it is shown that R can decompose over [ R , R ] , as R = F x + [ R , R ] , for a fixed element x ∈ R . The space R / [ R , R ] over F is known as the Whitehead space of R . When R is a semisimple central F -algebra, the dimension of its Whitehead space reveals the number of simple components of R . More precisely, we show that when R is algebraic over F and Char   F = 0 , then the number of simple components of R is greater than or equal to dim F     R / [ R , R ] , and when R is finite dimensional over F or is locally finite over F in the case of Char   F = 0 , then the number of simple components of R is equal to dim F     R / [ R , R ] .

Date: 2002
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/31/703505.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/31/703505.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:703505

DOI: 10.1155/S0161171202007998

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().