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.
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 of the symmetric group over a field of characteristic 0 (or ). The goal is to obtain a constructive version of the isomorphism where is a partition of and counts the standard tableaux of shape ....
Certaines relations binaires sont définies sur les demi-groupes et les demi-groupes à involution. On examine comment elles peuvent en ordonner les éléments: notamment les idempotents, les éléments réguliers au sens de von Neumann, ceux qui possédent un inverse ponctuel ou de Moore-Penrose ; et en fonction aussi de conditions sur l'involution. Ces relations peuvent alors coïncider avec les ordres naturels des idempotents et des demi-groupes inverses, avec les ordres de Drazin et de Hartwig : elles...
We introduce sturdy frames of type (2,2) algebras, which are a common generalization of sturdy semilattices of semigroups and of distributive lattices of rings in the theory of semirings. By using sturdy frames, we are able to characterize some semirings. In particular, some results on semirings recently obtained by Bandelt, Petrich and Ghosh can be extended and generalized.
We show that there is a one-to-one correspondence between basic cotilting complexes and certain contravariantly finite subcategories of the bounded derived category of an artin algebra. This is a triangulated version of a result by Auslander and Reiten. We use this to find an existence criterion for complements to exceptional complexes.
Si supponga che l'anello ammetta una decomposizione come prodotto subdiretto di anelli , tali che per si abbia (), e sia . Si scelga un -modulo (destro) che sia libero da torsione rispetto ad , cioè ; allora può essere rappresentato come prodotto subdiretto irridondante degli -moduli liberi da torsione rispetto ad . Si fa uno studio di un subprodotto generale di una classe di -moduli