Skew Hurwitz Polinom Halkası Terslenebilir Olan Halkalar ve Genişlemeleri

Year 2020, Volume: 20 Issue: 6, 983 - 990, 31.12.2020

Fatma Kaynarca

https://doi.org/10.35414/akufemubid.746509

Abstract

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

Keywords

Terslenebilir halka, Skew Hurwitz polinom halkası, Zayıf SH-terslenebilir halka, α-katı halka

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

Abstract

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.

Keywords

Reversible ring, Skew Hurwitz polynomial ring, Weak SH-reversible ring, α-rigid ring

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