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Invertible ideals and Gaussian semirings

Shaban Ghalandarzadeh, Peyman Nasehpour, Rafieh Razavi (2017)

Archivum Mathematicum

In the first section, we introduce the notions of fractional and invertible ideals of semirings and characterize invertible ideals of a semidomain. In section two, we define Prüfer semirings and characterize them in terms of valuation semirings. In this section, we also characterize Prüfer semirings in terms of some identities over its ideals such as ( I + J ) ( I J ) = I J for all ideals I , J of S . In the third section, we give a semiring version for the Gilmer-Tsang Theorem, which states that for a suitable family...

Jordan ideals and derivations in prime near-rings

Abdelkarim Boua, Lahcen Oukhtite, Abderrahmane Raji (2014)

Commentationes Mathematicae Universitatis Carolinae

In this paper we investigate 3 -prime near-rings with derivations satisfying certain differential identities on Jordan ideals, and we provide examples to show that the assumed restrictions cannot be relaxed.

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