Displaying similar documents to “The rank of G0 for polycyclic group algebras”

Co-rank and Betti number of a group

Irina Gelbukh (2015)

Czechoslovak Mathematical Journal

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For a finitely generated group, we study the relations between its rank, the maximal rank of its free quotient, called co-rank (inner rank, cut number), and the maximal rank of its free abelian quotient, called the Betti number. We show that any combination of the group's rank, co-rank, and Betti number within obvious constraints is realized for some finitely presented group (for Betti number equal to rank, the group can be chosen torsion-free). In addition, we show that the Betti number...

Trace and determinant in Banach algebras

Bernard Aupetit, H. Mouton (1996)

Studia Mathematica

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We show that the trace and the determinant on a semisimple Banach algebra can be defined in a purely spectral and analytic way and then we obtain many consequences from these new definitions.

A new rank formula for idempotent matrices with applications

Yong Ge Tian, George P. H. Styan (2002)

Commentationes Mathematicae Universitatis Carolinae

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It is shown that rank ( P * A Q ) = rank ( P * A ) + rank ( A Q ) - rank ( A ) , where A is idempotent, [ P , Q ] has full row rank and P * Q = 0 . Some applications of the rank formula to generalized inverses of matrices are also presented.

Notes on a class of simple C*-algebras with real rank zero.

Kenneth R. Goodearl (1992)

Publicacions Matemàtiques

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A construction method is presented for a class of simple C*-algebras whose basic properties -including their real ranks- can be computed relatively easily, using linear algebra. A numerival invariant attached to the construction determines wether a given algebra has real rank 0 or 1. Moreover, these algebras all have stable rank 1, and each nonzero hereditary sub-C*-algebra contains a nonzero projection, yet there are examples in which the linear span of the projections is not dense....

From geometry to invertibility preservers

Hans Havlicek, Peter Šemrl (2006)

Studia Mathematica

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We characterize bijections on matrix spaces (operator algebras) preserving full rank (invertibility) of differences of matrix (operator) pairs in both directions.