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On near-ring ideals with ( σ , τ ) -derivation

Öznur Golbaşi, Neşet Aydin (2007)

Archivum Mathematicum

Let N be a 3 -prime left near-ring with multiplicative center Z , a ( σ , τ ) -derivation D on N is defined to be an additive endomorphism satisfying the product rule D ( x y ) = τ ( x ) D ( y ) + D ( x ) σ ( y ) for all x , y N , where σ and τ are automorphisms of N . A nonempty subset U of N will be called a semigroup right ideal (resp. semigroup left ideal) if U N U (resp. N U U ) and if U is both a semigroup right ideal and a semigroup left ideal, it be called a semigroup ideal. We prove the following results: Let D be a ( σ ,

On p-semirings

Branka Budimirović, Vjekoslav Budimirović, Branimir Šešelja (2002)

Discussiones Mathematicae - General Algebra and Applications

A class of semirings, so called p-semirings, characterized by a natural number p is introduced and basic properties are investigated. It is proved that every p-semiring is a union of skew rings. It is proved that for some p-semirings with non-commutative operations, this union contains rings which are commutative and possess an identity.

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