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Rickart’s theorem states that every bijective multiplicative mapping of a Boolean ring  R onto an arbitrary ring  S is necessarily additive. We prove a version of Rickart’s theorem for non-bijective mappings. This enables us to partially answer a question that was left open (Al Subaiei, B., Jarboui, N. On the Monoid of Unital Endomorphisms of a Boolean Ring. Axioms 2021, 10, 305).

A Rickart-Like Theorem for the Additivity of Multiplicative Maps on Rings