Let A be a semisimple alternative superalgebra over a field of characteristic not 2, 3 which contains no sub-superalgebras of type (M1(F), M1(F)) in its decomposition into prime ideals. Then each superbimodule of A is merely an alternative A-bimodule. The case where A = (M1(F),M1(F)) produces, however, a series of indecomposable A-superbimodules. In the present article, we describe such superbimodules over an algebraically closed field.
KeywordsPresent Article Mathematical Logic Prime Ideal Alternative Superalgebra
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- 1.R. D. Schafer, “Representation of alternative algebras,”Trans. Am. Math. Soc.,72, No. 1, 1–17 (1952).Google Scholar
- 2.N. Jacobson, “Structure of alternative and Jordan bimodules,”Osaka J. Math.,6, No. 1, 1–71 (1954).Google Scholar
- 3.N. A. Pisarenko, “The Wedderburn decomposition in finite-dimensional alternative superalgebras,”Algebra Logika,32, No. 4, 428–440 (1993).Google Scholar
- 4.R. S. Pierce,Associative Algebras, Springer, New York (1982).Google Scholar
- 5.E. I. Zelmanov and I. P. Shestakov, “Prime alternative superalgebras and nilpotency of the radical of the free nilpotent algebra,”Izv. Akad. Nauk SSSR, Ser. Mat.,54, No. 4, 676–693 (1990).Google Scholar
- 6.A. R. Kemer, “Identities of associative algebras are finitely based,”Algebra Logika,26, No. 5, 597–641 (1987).Google Scholar
- 7.The Dnestrov Notebook, Unsolved Problems in the Theory of Rings and Modules, 4th edn., Novosibirsk (1993).Google Scholar