Some Basic Properties of Weakly Classical Primary and Classical Primary Subsemimodules in Semimodules
Keywords:semimodule, classical primary subsemimodule, weakly classical primary subsemimodule, -subsemimodule, primary ideal.
In this paper, we study classical primary and weakly classical primary subsemimodules in semimodules over a semirings. Some characterizations of classical primary and weakly classical primary subsemimodules are obtained. Moreover, we investigate relationships classical primary and weakly classical primary subsemimodules in semimodules over a semirings. Finally, we obtain necessary and sufficient conditions of a weakly classical primary to be a classical primary.
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