Displaying similar documents to “Congruences and ideals in ternary rings”

When is every order ideal a ring ideal?

Melvin Henriksen, Suzanne Larson, Frank A. Smith (1991)

Commentationes Mathematicae Universitatis Carolinae

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A lattice-ordered ring ℝ is called an if each of its order ideals is a ring ideal. Generalizing earlier work of Basly and Triki, OIRI-rings are characterized as those f -rings ℝ such that ℝ / 𝕀 is contained in an f -ring with an identity element that is a strong order unit for some nil l -ideal 𝕀 of ℝ . In particular, if P ( ℝ ) denotes the set of nilpotent elements of the f -ring ℝ , then ℝ is an OIRI-ring if and only if ℝ / P ( ℝ ) is contained in an f -ring with an identity element that is a strong order unit. ...

On the lattice of congruences on inverse semirings

Anwesha Bhuniya, Anjan Kumar Bhuniya (2008)

Discussiones Mathematicae - General Algebra and Applications

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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...

On presentations of semigroup rings

Mario Petrich, Pedro V. Silva (1999)

Bollettino dell'Unione Matematica Italiana

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Siano I un ideale di un anello R e σ una congruenza su un semigruppo S . Consideriamo l'anello semigruppo R / I ⁢ S / σ come un'immagine omomorfa dell'anello semigruppo R ⁢ S . Questo è fatto in tre passi: prima studiando l'anello semigruppo R ⁢ S / σ , poi R / I ⁢ S e infine combinando i due casi speciali. In ciascun caso, determiniamo l'ideale che è il nucleo dell'omomorfismo in questione. I risultati corrispondenti per le C -algebre, dove C è un anello commutativo, possono essere facilmente dedotti. Alcuni raffinamenti,...