Group Rings – A Brief History and some their Generalizations

We give a brief exposition of the history of the group rings and some their generalizations. Also we indicate some information of certain problems and results.

Acoustic Riddles of Cultural Heritage

It is shown, that in the process of evolution, a relationship between some hidden parameters of acoustic signals and expected emotional response to them has been formed. This relationship is a necessary condition for a living creature to survive. The efficiency of the concept represented is illustrated using examples from the field of classical music, ethnic African music, as well as biolinguistic signals of animals. Reasons of a particular impact of bell rings are analyzed using acoustic signals of some Bulgarian and Russian bell rings and chimes.

Binomial Skew Polynomial Rings, Artin-Schelter Regularity, and Binomial Solutions of the Yang-Baxter Equation

2000 Mathematics Subject Classification: Primary 81R50, 16W50, 16S36, 16S37.

On Parabolic Subgroups and Hecke Algebras of some Fractal Groups

* The authors thank the “Swiss National Science Foundation” for its support.

Isomorphism of Commutative Group Algebras of Finite Abelian Groups

Let a commutative ring R be a direct product of indecomposable rings with identity and let G be a finite abelian p-group. In the present paper we give a complete system of invariants of the group algebra RG of G over R when p is an invertible element in R. These investigations extend some classical results of Berman (1953 and 1958), Sehgal (1970) and Karpilovsky (1984) as well as a result of Mollov (1986).

Zero-Dimensionality and Serre Rings

2000 Mathematics Subject Classification: Primary 13A99; Secondary 13A15, 13B02, 13E05.

Involution Matrix Algebras – Identities and Growth

2000 Mathematics Subject Classification: 16R50, 16R10.

Normal and Normally Outer Automorphisms of Free Metabelian Nilpotent Lie Algebras

2000 Mathematics Subject Classification: 17B01, 17B30, 17B40.