The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “Real commutative algebra (I). Places.”

Trace and determinant in Banach algebras

Bernard Aupetit, H. Mouton (1996)

Studia Mathematica

Similarity:

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.

Finite rank elements in semisimple Banach algebras

Matej Brešar, Peter Šemrl (1998)

Studia Mathematica

Similarity:

Let A be a semisimple Banach algebra. We define the rank of a nonzero element a in the socle of A to be the minimum of the number of minimal left ideals whose sum contains a. Several characterizations of rank are proved.

Co-rank and Betti number of a group

Irina Gelbukh (2015)

Czechoslovak Mathematical Journal

Similarity:

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...