Semirings applications : 9783639710144 : 16 Feb 2014 : The subject material in the book is presented in Five Chapters. In the First Chapter, we study the relation between Smarandache semirings and many-valued logics, in particular Basic logic and Lukasiewicz logic. We will also definitions of Smarandache semirings, automata on BL - algebras and MV- algebra. In the Second Chapter, we study the action of Legendre's polynomials on commutative finite rings R, semirings, positively ordered commutative semirings and some other semirings. The rings Fq , Z/nZ where n is an RSA integer and commutative sub rings o f Matn (Fq) are the main examples. We study the difficulty of discrete Legendre's problem in these rings and prove several equivalence results. In the Third Chapter, we deal, with Smaandache loops, sub loops, Smarandache sub loops, normal loops, Smarandache normal loops, the structure of Moufang loops and Paige. We analyze DLP (Discrete Logirithm Problem) in the Paige loop M* (q),