Some results on subtractive ideals in semirings

This paper is concerned with generalizing some results of ringtheory ro semiring theory. Throughout this paper a semiring willbe defined as follows: A semiring is a set $R$ together with twobinary operations called addition ``$+$'' and multiplication``$.$'' such that $(R, +)$ is a commutative semigroup and $(R, .)$is semigroup; connecting the two algebraic structures are thedistrubutive laws: $a (b+ c)= ab+ ac$ and $(b+ c) a= ba+ ca$ forall $a, b, cin R$.