On the Classical Primary Radical Formula and Classical Primary Subsemimodules
Keywords:
classical primary subsemimodule, primary subsemimodule, classical primary radical, classical primary radical formula.Abstract
In this paper, we characterize the classical primary radical of subsemimodules and classical primary subsemimodules of semimodules over a commutative semirings. Furthermore we prove that if  $N_{j}$ is a classical primary subsemimodule of  $M_{j}$ then $N_{j}$ is to satisfy the classical primary radical formula in $M_{j}$ if and only if $M{1}\times M_{2}\times\ldots \times M_{J-1} \times N_{j}\timesM_{j+1}\times\ldots\times M_{n}$  is to satisfy the classical primary radical formula in $M$.
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