University of Guilan Journal of Algebra and Related Topics 2345-3931 9 1 2021 06 01 On Prime and semiprime ideals of $\Gamma$-semihyperrings 131 141 4815 10.22124/jart.2021.17550.1226 EN J. J. Patil Indraraj ACS college, Sillod, Dr. B. A. M. University, Aurangabad, India K. Pawar Department of Mathematics, School of Mathematical Sciences, Kavayitri Bahinabai Chaudhari North Maharashtra University, Jalgaon, India Journal Article 2020 09 03 The $\Gamma$-semihyperring is  a generalization of the concepts of a semiring, a semihyperring and a $\Gamma$-semiring. In this paper, the notions of completely prime ideals and prime radicals for $\Gamma$-semihyperring are introduced and studied some important properties accordingly. We also introduced the notions of $m$-system and complete $m$-system. Then characterizations of prime ideals and completely prime ideals of $\Gamma$-semihyperring with the help of $m$-system and complete $m$-system has been taken into account. It is our attempt to find a bridge between semiprime (completely semiprime) ideals and prime (completely prime) ideals of a $\Gamma$-semihyperring. https://jart.guilan.ac.ir/article_4815_117fc818cdcd0118bbbd941684ac8756.pdf