Abstract
We investigate quasi-algebrasF with zero divisors of dimension 2 over a commutative fieldK which have aK-basis 1,j with an idealKj. Assume thatj belongs to the nucleus ofF. Ifj is an idempotent (and can not be replaced by a nilpotent element) thenF is an algebra, i.e. satisfies both distributative laws. Ifj is nilpotent the possibilities forf depend on the solution of a functional equation first studied by Gołab and Schinzel for the field of real numbers. We discuss this functional equation in arbitrary locally compact fields.
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Plaumann, P., Strambach, K. Zweidimensionale Quasialgebren mit Nullteilern. Aeq. Math. 15, 249–264 (1977). https://doi.org/10.1007/BF01835655
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DOI: https://doi.org/10.1007/BF01835655