TY - JOUR AU - Yiarayong, Pairote AU - Panpho, Phakakorn PY - 2014/10/15 Y2 - 2024/03/28 TI - On the Classical Primary Radical Formula and Classical Primary Subsemimodules JF - Asian Journal of Applied Sciences JA - AJAS VL - 2 IS - 5 SE - Articles DO - UR - https://ajouronline.com/index.php/AJAS/article/view/1780 SP - AB - <p>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 $M$.</p> ER -