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On ternary semifields

Tapan K. Dutta, Sukhendu Kar (2004)

Discussiones Mathematicae - General Algebra and Applications

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.

On the lattice of congruences on inverse semirings

Anwesha Bhuniya, Anjan Kumar Bhuniya (2008)

Discussiones Mathematicae - General Algebra and Applications

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 ρ m i n , ρ m a x , ρ m i n and ρ m a x on S and showed that ρ θ = [ ρ m i n , ρ m a x ] and ρ κ = [ ρ m i n , ρ m a x ] . Different properties of ρθ and ρκ have been considered here. A congruence ρ on S is a Clifford congruence if and only if ρ m a x is a distributive lattice congruence and ρ m a x is a skew-ring congruence on S. If η (σ) is the least distributive...

On uniformly strongly prime Γ-semirings (II)

Tapan Kumar Dutta, Suhrid Dhara (2006)

Discussiones Mathematicae - General Algebra and Applications

The Uniformly strongly prime k-radical of a Γ-semiring is a special class which we study via its operator semiring.

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