A short proof of the characterization of idempotent subreducts of semimodules over commutative semirings is presented. It says that an idempotentalgebra embeds into a semimodule over a commutative semiring, if and only if it belongs to the variety of Szendrei modes.
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David Stankovský, Idempotent Subreducts of Semimodules over Commutative Semirings. Rend. Sem. Mat. Univ. Padova 121 (2009), pp. 33–43DOI 10.4171/RSMUP/121-3