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Irreducible binary (−1, 1)-bimodules over simple finite-dimensional algebras

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Abstract

We prove that an irreducible binary (−1, 1)-bimodule over A is alternative in the following cases: (a) A is a composition algebra over a field of characteristic other than 2 and 3; (b) A is a simple finite-dimensional alternative algebra over a field of characteristic 0.

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References

  1. Zhevlakov K. A., Slin’ko A. M., Shestakov I. P., and Shirshov A. I., Rings That Are Nearly Associative, Academic Press, New York (1982).

    MATH  Google Scholar 

  2. Jacobson N., “Structure and representations of Jordan algebras,” Amer. Math. Soc. Colloq. Publ., 39 (1968).

  3. Shestakov I. P., “Prime alternative superalgebras of arbitrary characteristic,” Algebra and Logic, 36, No. 6, 389–412 (1997).

    MATH  MathSciNet  Google Scholar 

  4. Mikheev I. M., “Simple right alternative rings,” Algebra and Logic, 16, No. 6, 456–476 (1977).

    Article  MATH  Google Scholar 

  5. Skosyrskii V. G., “Right alternative algebras,” Algebra and Logic, 23, No. 2, 131–136 (1984).

    Article  MATH  MathSciNet  Google Scholar 

  6. Murakami L. and Shestakov I., “Irreducible unital right alternative bimodules,” J. Algebra, 246, No. 2, 897–914 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  7. Hentzel I. R., “Nil semi-simple locally (−1, 1) rings,” Bull. Iranian Math. Soc., 9, 11–14 (1981).

    MathSciNet  Google Scholar 

  8. Hentzel I. R. and Smith H. F., “Simple locally (−1, 1) nil rings,” J. Algebra, 101, 262–272 (1986).

    Article  MATH  MathSciNet  Google Scholar 

  9. Pchelintsev S. V., “Defining identities of a certain variety of right alternative algebras,” Mat. Zametki, 20, No. 2, 161–176 (1976).

    MATH  MathSciNet  Google Scholar 

  10. Pchelintsev S. V., “On central ideals of finitely generated binary (−1, 1)-algebras, ” Sb. Math, 193, No. 3–4, 585–607 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  11. Pchelintsev S. V., “Nilpotency of the alternator ideal of a finitely generated binary (−1, 1)-algebra,” Siberian Math. J., 45, No. 2, 356–375 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  12. Hentzel I. R., “The characterization of (−1, 1) rings,” J. Algebra, 30, 236–258 (1974).

    Article  MATH  MathSciNet  Google Scholar 

  13. Pchelintsev S. V., “A free (−1, 1)-algebra with two generators,” Algebra i Logika, 13, No. 4, 425–449 (1974).

    MATH  MathSciNet  Google Scholar 

  14. Kuz’min E. N. and Shestakov I. P., “Non-associative structures,” Algebra VI. Encycl. Math. Sci., 57, 197–280 (1995).

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Finance Academy of the Government of the Russian Federation, Moscow, Russia

    S. V. Pchelintsev

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  1. S. V. Pchelintsev
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__________

Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 47, No. 5, pp. 1139–1146, September–October, 2006.

Original Russian Text Copyright © 2006 Pchelintsev S. V.

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Pchelintsev, S.V. Irreducible binary (−1, 1)-bimodules over simple finite-dimensional algebras. Sib Math J 47, 934–939 (2006). https://doi.org/10.1007/s11202-006-0104-8

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  • DOI: https://doi.org/10.1007/s11202-006-0104-8

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