Cyclization of n-alkylazinium cations with bisnucleophiles. 4. Regio- and stereospecificity of the reactions of β-diketones with quinoxalinium salts and their aza and benzo analogs

The reactions of substituted quinoxalinium, benzo[g]- and benzo[f]quinoxalinium, and pyrido[2,3-b]pyrazinium salts with anions of -dicarbonyl compounds give furo[2,3-b]-annelated systems with strictly determined regio- and stereoorientations.See [1] for Communication 3.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 11, pp. 1543–1548, November, 1981.     

Semisimplicity of the algebra of indecomposable representations of a finite commutative semigroup

Finite semigroups S, having only a finite number of indecomposable matrix representations over a field K of characteristic are considered. It is proved that the algebra over the field F of K-representations of the semigroup S is semisimple if and only if for any maximal subgroup of the semigroup S the characteristic of the field F does not divide the index of its Sylow p-subgroup and is greater than the order of this Sylow subgroup.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 57, pp. 125–128, 1976.     

Cyclization of N-alkylazinium cations with bisnucleophiles. 6. Cycloelimination of tetrahydro-endo-furo[2,3-b]quinoxalines leading to 2,3-disubstituted tetrahydroquinoxalines

The reaction of an N-methylquinoxalinium salt with a -diketone under thermodynamic-control conditions leads to 2,3-disubstituted tetrahydroquinoxaline via cycloelimination of the initially formed tetrahydro-endo-furo[2,3-b]quinoxaline.See [1] for communication 5.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 10, pp. 1410–1416, October, 1982.     

Algebras with a finite number of classes of nonequivalent indecomposable modules

It is proved that the class of finite-dimensional algebras over fields with the property stated in the title is closed with respect to extensions by means of semi-simple artinian algebras.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 132, pp. 122–128, 1983.     

Cyclizations of N-alkyl-substituted azinium cations with bifunctional nucleophiles. 28. Orientation of the nucleophile in the reaction of quinoxalinium salts with indan-1,3-dione

In reactions with quinoxalinium salts in alcoholic-base media indan-1,3-dione acts as a C nucleophile, adding at the 2 or 3 position of the heterocycle to give the corresponding ylidene derivatives; attack by the nucleophile at the C₍₃₎ atom (the position relative to the quaternary nitrogen atom) is preceded by addition of alcohol at the a position. Dissociative substitution at the C₍₂₎ atom in 2-alkoxy-3-(1,3-dioxoindan-2-ylidene)-1,2,3,4-tetrahydroquinoxalines by another nucleophile makes it possible to regard lyate complexes as probable intermediates in cyclizations of 1,4-diazinium salts with dinucleophiles.See [1] for Communication 27.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 5, pp. 667–674, May, 1990.     

Formation of soot clusters under the action of electric field of direct-current corona during combustion of natural gas

The influence of the electrode type and geometry, the interelectrode distance, and the electric field strength on the yield and distribution of soot particles during the combustion of natural gas in an electric field of direct-current corona discharge for positive and negative electrodes has been studied. The results are interpreted with allowance for the ion wind effect. The structure of soot clusters has been examined by electron microscopy.     

Cyclization of N-alkylazinium cations with bifunctional nucleophiles. 25. Oxidation of tetrahydroquinoxalines condensed with six-membered ring heterocycles

Reaction of six-membered ring heterocycle-annulated tetrahydroquinoxalines with potassium permanganate in acetone results in the formation of oxidation products containing a common system of conjugated double bonds.For Communication 24, see Ref. [1].Translated from Khimiya Geterotsklicheskikh Soedinenii, No. 9, pp. 1260–1263, September, 1987.     

Bi-Ideals in Ordered Semigroups and Ordered Groups

It is shown that an ordered semigroup is right and left simple if and only if it does not contain proper bi-ideals. An example showing that an ordered semigroup without proper bi-ideals need not be an ordered group is constructed. Bibliography: 7 titles.