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s -weakly regular group rings

W. B. Vasantha Kandasamy (1993)

Archivum Mathematicum

In this note we obtain a necessary and sufficient condition for a ring to be s -weakly regular (i) When R is a ring with identity and without divisors of zero (ii) When R is a ring without divisors of zero. Further it is proved in a s -weakly regular ring with identity and without units every element is a zero divisor.

Some counter-examples in the theory of the Galois module structure of wild extensions

Stephen M. J. Wilson (1980)

Annales de l'institut Fourier

Considering the ring of integers in a number field as a Z Γ -module (where Γ is a galois group of the field), one hoped to prove useful theorems about the extension of this module to a module or a lattice over a maximal order. In this paper it is show that it could be difficult to obtain, in this way, parameters which are independent of the choice of the maximal order. Several lemmas about twisted group rings are required in the proof.

Structure of the Unit Group of FD10

Khan, Manju (2009)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 16U60, 20C05.The structure of the unit group of the group algebra FD10 of the dihedral group D10 of order 10 over a finite field F has been obtained.Supported by National Board of Higher Mathematics, DAE, India.

Structure theory for the group algebra of the symmetric group, with applications to polynomial identities for the octonions

Murray R. Bremner, Sara Madariaga, Luiz A. Peresi (2016)

Commentationes Mathematicae Universitatis Carolinae

This is a survey paper on applications of the representation theory of the symmetric group to the theory of polynomial identities for associative and nonassociative algebras. In §1, we present a detailed review (with complete proofs) of the classical structure theory of the group algebra 𝔽 S n of the symmetric group S n over a field 𝔽 of characteristic 0 (or p > n ). The goal is to obtain a constructive version of the isomorphism ψ : ⨁ λ M d λ ( 𝔽 ) ⟶ 𝔽 S n where λ is a partition of n and d λ counts the standard tableaux of shape λ ....

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