Identities of finitely generated graded algebras with involution

We consider associative algebras with involution graded by a finite abelian group G over a field of characteristic zero. Suppose that the involution is compatible with the grading. We represent conditions permitting PI-representability of such algebras. Particularly, it is proved that a finitely generated (Z/qZ)-graded associative PI-algebra with involution satisfies exactly the same graded identities with involution as some finite dimensional (Z/qZ)-graded algebra with involution for any prime q or q = 4. This is an analogue of the theorem of A.Kemer for ordinary identities, and an extension of the result of the author for identities with involution. The similar results were proved also recentely for graded identities

Finitely generated algebras with involution and their identities

Associative algebras with involution over a field of zero characteristic are considered. It is proved that in this case for any finitely generated associative algebra with involution there exists a finite dimensional algebra with involution which satisfies exactly the same identities with involution

Finite basis problem for identities with involution

We consider associative algebras with involution over a field of characteristic zero. We proved that any algebra with involution satisfies the same identities with involution as the Grassmann envelope of some finite dimensional $Z_4$-graded algebra with graded involution. As a consequence we obtain the positive solution of the Specht problem for identities with involution: any associative algebra with involution over a field of characteristic zero has a finite basis of identities with involution. These results are analogs of theorems of A.R.Kemer for ordinary identities

Influence of initial defects on defect formation process in ion doped silicon

We study the influence of initial defects in high-resistance epitaxial silicon layers of high-resistance epitaxial silicon structures on defect formation processes at ion boron doping. The method of reverse voltage-capacitance characteristics revealed two maxima of dopant concentration in epitaxial silicon layers ion-doped by boron. Studing the structure of the near-surface area in ion-doped epitaxial silicon by means of modern methods has shown that in the field of the first concentration maximum (the nearest one to a wafer surface), the fine-blocked silicon structure is localised. In the range of the second doping concentration maximum, the grid of dislocations with the variable period within one grid and consisting of 60° dislocations is found out. In the area of dislocation grids, oxygen atoms have been found out. The variable period in the grid is related with a change of mechanical stress and deformation distribution law in the plane of dopant diffusion front as dependent on the presence of initial defects in silicon