Levi and Malcev Theorems for Finite-Dimensional Algebras from the Variety Defined by the Identities x2 =J(x,y, zu) =0

We study the variety of binary Lie algebras defined by the identities x2 =J(x,y,zu) =0,where J(a,b,c) denotes the Jacobian of a,b,c.Building on previous work by Carrillo,Rasskazova,Sabinina and Grishkov,in the present article it is shown that the Levi and Malcev theorems hold for this variety of algebras.     

Isomerization ofn-butane on the SO4/ZrO2 catalyst promoted by IV Period metals

The catalytic activity of superacidic systems based on SO₄/ZrO₂ and modified by IV Period metals in isomerization ofn-butane was studied. At low temperatures of the reaction, the introduction of Fe³⁺, Sc³⁺, Co²⁺, or Zn²⁺ ions (1%) increases the yield of isobutane by 1.5 times due to the activation ofn-butane on the sites created by the promoting ions. The addition of Cr³⁺, V⁴⁺, or Mn²⁺ (1%) decreases the catalytic activity because of a decrease in the catalyst acidity, most likely, due to the reduction of surface sulfur species. The influence of the nature of the support and surface additives of SiO₂, TiO₂, and ZrO₂ on the activity and selectivity of the catalytic system inn-butane isomerization was studied. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7 pp. 1276–1280, July, 1999     

3,3,6-trimethylcycloheptanone

Conclusions 3,3,6-Trimethylcycloheptanone was synthesized for the first time and its properties were described.     

The question of the crotonic condensation of some cycloalkanones in the presence of oxides and carbonate of manganese

Conclusions Under the influence of carbonate and oxides of manganese, cyclopentanone undergoes crotonic condensation with the formation of-cyclopentylidenecyelopentanone; cycloheptanone, under the same conditions, remains practically unchanged.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 12, pp. 2831–2832, December, 1969.