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Isotopes of simple algebras of arbitrary dimension
Preview AbstractIt is proved that every finite-dimensional algebra is embeddable in a simple finite-dimensional algebra (a suitable isotope of a matrix algebra). An isotope of the 2nd order matrix algebra over an infinite extension of the ground field may contain a trivial ideal.
Every one-sided isotope of a simple unital alternative or Jordan algebra is a simple algebra. Besides, any isotope of a central simple non-Lie Maltsev algebra of characteristic other than 2 and 3 is a simple algebra. But an isotope of a simple Jordan algebra of the symmetric bilinear form on the infinite dimensional space may contain a trivial ideal.