Finitely generated semirings and semifields

We investigate commutative semirings, which are formed by a ground set equipped with two binary associative and commutative operations such that one distributes over the other. We narrow down our interest to ideal-simple semirings, that is, semirings without proper ideals. We present the classification of ideal-simple semirings and deal with some classes of ideal-simple semirings, namely semifields and parasemifields. The main result of this thesis is giving tight bounds on the minimal number of generators needed to generate a parasemifield as a semiring. We also study how the semifields that are finitely generated as a semiring look like. Last, but not least, we show that every finitely generated ideal-simple semiring is finitely-generated as a multiplicative semigroup