On Bernstein Algebras Satisfying Chain Conditions

REFERENCES

• Anderson , D. D. ( 1977 ). Artinian modules are countably generated . Colloq. Math. 38 : 5 – 6 .
   Google Scholar
• Baeza , R. ( 1990 ). On nuclear Bernstein algebras . Lin. Alg. Appl. 142 : 19 – 22 .
   Web of Science ®Google Scholar
• Beachy , J. A. ( 1999 ). Introductory Lectures on Rings and Modules . London Mathematical Society Student Texts 47 .
   Google Scholar
• Benslimane , M. , Boudi , N. ( 1997 ). Alternative Noetherian Banach algebras . Extrata Math. 12 : 41 – 46 .
   Google Scholar
• Benslimane , M. , Boudi , N. ( 1998 ). Noetherian Jordan Banach algebras are finite-dimensional . J. Algebra 213 : 340 – 350 .
   Google Scholar
• Costa , R. , Guzzo , H. Jr . ( 1993 ). Indecomposable baric algebras . Linear Algebra Appl. 183 : 223 – 236 .
   Web of Science ®Google Scholar
• Fuchs , L. ( 1969 ). Torsion preradicals and ascending Loewy series of modules . J. Reine Angew. Math. 239/240 : 169 – 179 .
   Google Scholar
• González , S. , Martínez , C. ( 1994 ). On Bernstein algebras . Nonassociative Algebras and Its Applications . Netherlands : Kluwer Academic Publishers , pp. 164 – 171 .
   Google Scholar
• Grishkov , A. N. ( 1987 ). On the genetic property of Bernstein algebras . Soviet Math. Dokl. 35 : 489 – 492 .
   Google Scholar
• Hentzel , I. R. , Peresi , L. A. ( 1989 ). Semi-prime Bernstein algebras . Arch. Math. 52 : 539 – 543 .
   Web of Science ®Google Scholar
• Hentzel , I. R. , Jacobs , D. P. , Peresi , L. A. , Sverchkov , S. R. ( 1994 ). Solvability of the ideal of all weight zero elements of a Bernstein algebra . Comm. Algebra 22 ( 9 ): 3265 – 3275 .
   Web of Science ®Google Scholar
• Holgate , P. ( 1975 ). Genetic algebras satisfying Bernstein's stationarity principle . J. London Math. Soc. 9 : 613 – 623 .
   Web of Science ®Google Scholar
• Koulibaly , A. , Ouattara , M. ( 1991 ). Structure et théorie de Frattini d'une algèbre de Bernstein . Alg. Groups Geom. 8 : 145 – 158 .
   Google Scholar
• Krapivin , A. A. ( 1992 ). An indicator of the geneticism of finitely generated Bernstein algebras . Sib. Math. J. 32 : 499 – 515 .
   Web of Science ®Google Scholar
• Lyubich , Yu. I. ( 1971 ). Basic concepts and theorems of evolutionary genetic for free populations . Russian Math. Surveys 26 ( 5 ): 51 – 123 .
   Google Scholar
• Lyubich , Yu. I. ( 1992 ). Mathematical Structures in Population Genetic. Springer-Verlag .
   Google Scholar
• Lyubich , Yu. I. ( 2000 ). Banach-Bernstein algebras and their applications . In: Nonassociative Algebra and Its Applications . Proceedings of the Fourth International Conference. Lect. Notes Pure Appl. Math. 211 . Sao Paulo, Brazil, New York : Dekker , pp. 205 – 210 .
   Google Scholar
• Medvedev , Yu. A. , Zel'manov , E. I. ( 1985 ). Solvable Jordan algebras . Comm. Algebra 13 ( 6 ): 1389 – 1414 .
   Web of Science ®Google Scholar
• Micali , A. , Ouattara , M. ( 1995 ). Structure des algèbres de Bernstein . Lin. Alg. Appl. 218 : 77 – 88 .
   Google Scholar
• Odoni , R. W. K. , Stratton , A. E. ( 1988 ). Structure of Bernstein algebras . Cahiers Math. Montpellier 37 : 117 – 125 .
   Google Scholar
• Peresi , L. A. (1991). Nilpotency in Bernstein algebras. Arch. Math. 56:437–439.
   Web of Science ®Google Scholar
• Shirshov , A. I. ( 1957 ). On some non-associative nil-rings and algebraic algebras (Russian) . Mat. Sb. 41 ( 83 ): 381 – 394 .
   Google Scholar
• Sinclair , A. M. , Tullo , W. ( 1974 ). Noetherian Banach algebras are finite-dimensional . Math. Ann. 21 : 151 – 153 .
   Google Scholar
• Suazo , A. ( 1999 ). On nuclear Bernstein algebras . Int. J. Math. Game Theory Algebra 8 ( 4 ): 207 – 212 .
   Google Scholar
• Wörz-Buzekros , A. ( 1980 ). Algebras in Genetics . Lecture Notes in Biomathematics, 36. Berlin, Heidelberg, New York : Springer-Verlag .
   Google Scholar
• Zel'manov , E. I. , Skosyrskii , V. G. ( 1983 ). Special Jordan nil-algebras of bounded index . Algebra and Logic 22 : 444 – 450 .
   Google Scholar
• Zhevlakov , K. A. , Slin'ko , A. M. , Shestakov , I. P. , Shirshov , A. I. ( 1982 ). Rings That Are Nearly Associative. New York : Academic Press .
   Google Scholar
• Communicated by I. P. Shestakov.
   Google Scholar