Skew Hurwitz Polinom Halkası Terslenebilir Olan Halkalar ve Genişlemeleri

Bu çalışmada; bir halkanın terslenebilir olması kavramı, o halka üzerine kurulan skew Hurwitzpolinomlar halkasına genişletilerek, zayıf skew Hurwitz terslenebilir (kısaca zayıf ??-terslenebilir) halkakavramı tanıtılmıştır. Bu halka sınıfının bazı özelikleri ve diğer halka sınıflarıyla ilişkileri incelenmiştir.Zayıf ??-terslenebilir halkaların bazı genişlemelerinin de zayıf ??-terslenebilir olup olmadığıaraştırılmıştır. Özel olarak, karakteristiği 0 olan bir ? halkası ve ?’nin bir ? monomorfizması için ?’ninzayıf ??-terslenebilir olması için gerek ve yeter koşul ?(?, ?) Jordan genişlemesinin zayıf ??-terslenebilir olması gerektiği ispatlanmıştır.

Rings Over Which Skew Hurwitz Polynomial Rings Are Reversible and Their Extensions

In this paper; the concept of the ability of a ring to be reversible is extended to the ring of skew Hurwitz polynomials established on that ring, and the concept of the weak skew Hurwitz reversible (briefly weak SH-reversible) ring is introduced. Some properties of this ring class and its relations with other ring classes are examined. It is also investigated whether some extension of weak SH-reversible rings are weak SH-reversible. In particular, it is proved that for a ring R with characteristic 0 and an α monomorphism of R the Jordan extension A (R, α) of R is weak SH-reversible if and only if R is weak SH-reversible.

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