Group Ring Idempotents with Minimal Trace

Idempotents in group algebras and minimal abelian codes

We compute the number of simple components of a semisimple finite abelian group algebra and determine all cases where this number is minimal; i.e. equal to the number of simple components of the rational group algebra of the same group. This result is used to compute idempotent generators of minimal abelian codes, extending results of Arora and Pruthi [S.K. Arora, M. Pruthi, Minimal cyclic code...

Smarandache Idempotents in finite ring Zn and in Group Ring ZnG

In this paper we analyze and study the Smarandache idempotents (S-idempotents) in the ring Zn and in the group ring ZnG of a finite group G over the finite ring Zn. We have shown the existance of Smarandache idempotents (S-idempotents) in the ring Zn when n = 2 p (or 3p), where p is a prime > 2 (or p a prime > 3). Also we have shown the existance of Smarandache idempotents (S-idempotents) in th...

Idempotents in Group Algebras

In this survey we collect and present the classical and some recent methods to compute the primitive (central) idempotents in semisimple group algebras. MSC 2010. 20C05, 20C15, 16S34, 16U60.

Central Idempotents in Group Algebras

IDEMPOTENTS IN GROUP RINGS By

It is then easily verified that RG satisfies the ring axioms; in fact, RG is a linear algebra over R. (We write all groups multiplicatively, and denote group identities by 1; we also use 1 for the unit element of R if there is one.) If R, in addition to being a ring, is a Banach algebra (i.e., an algebra over the complex field K, with a submultiplicative norm which makes R a Banach space), then...