Ideal theory in some ternary semirings

Abstract

In this thesis, we study the ideal theory in the ternary semiring Z₀[superscript +] of non-negative integers and the ternary semiring Z₀[superscript -] x Z₀[superscript -] of ordered pairs of non-positiveintegers and obtain some results regarding the ideals of these ternary semirings. Moreover, we show that the ternary semirings Z₀[superscript +] and Z₀[superscript -] are isomorphic as well as the ternary semirings Z₀[superscript +] x Z₀[superscript +] and Z₀[superscript -] x Z₀[superscript -]. We also compare the ternary semiring Z to the ring Z.