Boolean Rings that are Baire Spaces

∗ The present article was originally submitted for the second volume of Murcia Seminar on Functional Analysis (1989). Unfortunately it has been not possible to continue with Murcia Seminar publication anymore. For historical reasons the present vesion correspond with the original one.

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).

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.

Essential Cover and Closure

2000 Mathematics Subject Classification: 16N80, 16S70, 16D25, 13G05.