Abstract
The primary aim of this paper is to study mappings J of rings that are additive and that satisfy the conditions
Such mappings will be called Jordan homomorphisms. If the additive groups admit the operator 1/2 in the sense that 2x = a has a unique solution (1/2)a for every a, then conditions (1) are equivalent to the simpler condition
Mappings satisfying (2) were first considered by Ancochea [1], [2](1). The modification to (1) is essentially due to Kaplansky [13]. Its purpose is to obviate the necessity of imposing any restriction on the additive groups of the rings under consideration.
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© 1989 Birkhäuser Boston
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Jacobson, N., Rickart, C.E. (1989). Jordan Homomorphisms of Rings. In: Nathan Jacobson Collected Mathematical Papers. Contemporary Mathematicians. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3694-8_7
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DOI: https://doi.org/10.1007/978-1-4612-3694-8_7
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