On regular elements in an incline.
In this paper, we introduce the notion of ternary semi-integral domain and ternary semifield and study some of their properties.In particular we also investigate the maximal ideals of the ternary semiring Z¯₀.
Let S be a semiring whose additive reduct (S,+) is an inverse semigroup. The relations θ and k, induced by tr and ker (resp.), are congruences on the lattice C(S) of all congruences on S. For ρ ∈ C(S), we have introduced four congruences and on S and showed that and . Different properties of ρθ and ρκ have been considered here. A congruence ρ on S is a Clifford congruence if and only if is a distributive lattice congruence and is a skew-ring congruence on S. If η (σ) is the least distributive...
The Uniformly strongly prime k-radical of a Γ-semiring is a special class which we study via its operator semiring.