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The Socle of Semimodules Over MV-semirings
Aiping Gan, Antonio Di Nola and Yichuan Yang
An MV-semimodule is a left semimodule over an MV-semiring. We prove the homomorphism theorems of MV-semimodules, discuss the relations between simple MV-semimodules and maximal MV-subsemimodules, and the relations between superfluous MVsubsemimodules and essential MV-subsemimodules. Especially, we introduce and characterize the socles and the radicals of MVsemimodules.
2010 Mathematics Subject Classification. 16Y60, 06D35
Keywords: MV-algebras, MV-semirings, MV-semimodule, radical