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- W2000984834 abstract "Let k be an infinite field, I an infinite set, V a k-vector-space, and g:k^Ito V a k-linear map. It is shown that if dim_k(V) is not too large (under various hypotheses on card(k) and card(I), if it is finite, respectively countable, respectively < card(k)), then ker(g) must contain elements (u_i)_{iin I} with all but finitely many components u_i nonzero. These results are used to prove that any homomorphism from a direct product prod_I A_i of not-necessarily-associative algebras A_i onto an algebra B, where dim_k(B) is not too large (in the same senses) must factor through the projection of prod_I A_i onto the product of finitely many of the A_i, modulo a map into the subalgebra {bin B | bB=Bb={0}}subseteq B. Detailed consequences are noted in the case where the A_i are Lie algebras." @default.
- W2000984834 created "2016-06-24" @default.
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- W2000984834 date "2012-04-01" @default.
- W2000984834 modified "2023-09-30" @default.
- W2000984834 title "Linear maps on kI, and homomorphic images of infinite direct product algebras" @default.
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- W2000984834 doi "https://doi.org/10.1016/j.jalgebra.2012.01.004" @default.
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