Skew Hurwitz Polinom Halkası Terslenebilir Olan Halkalar ve Genişlemeleri

Yıl 2020, , 983 - 990, 31.12.2020

Fatma Kaynarca

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

Öz

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.

Anahtar Kelimeler

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

Öz

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.

Anahtar Kelimeler

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

Kaynakça

• Ahmadi, M., Moussavi, A. and Nourozi, V., 2014. On skew Hurwitz serieswise Armendariz rings. Asian-European Journal of Mathematics, 7(3), 1450036.
• Başer, M., Hong, C. Y. and Kwak, T. K., 2009. On extended reversible rings. Algebra Colloquium, 16(1), 37-48.
• Cohn, P. M., 1999. Reversible rings. Bulletin of the London Mathematical Society, 31, 641-648.
• Hashemi, E., Moussavi, A., 2005. Polynomial extensions of quasi-Baer rings, Acta Mathematica Hungarica, 3, 207-224.
• Hassanein, A. M., 2007. Clean rings of skew Hurwitz series, Le Mathematiche, 62(1), 47-54.
• Hassanein, A. M., 2012. On uniquely clean skew Hurwitz series, Southeast Asian Bulletin of Mathematics, 35, 5-10.
• Herstein, I. N., 1975. Topics in Algebra, Xerox College Publishing Lexington, Massachusetts Toronto, 1-388.
• Hong, C. Y., Kim, N. Y., Kwak, T. K., 2000. Ore extensions of Baer and p.p-rings, Journal of Pure and Applied Algebra, 151(3), 215-226.
• Jin, H. L., Kaynarca, F. and Kwak, T. K., Lee, Y. 2017. On commutativity of skew polynomials at zero. Bulletin of the Korean Mathematical Society, 54, 51-69.
• Jordan, D. A., 1982. Bijective extensions of injective rings endomorphism, Journal of the London Mathematical Society, 25(3), 435-448.
• Kaynarca, F., Yıldırım, M. A., 2020. Reversibility of skew Hurwitz series rings, accepted by Hacettepe Journal of Mathematics and Statistics.
• Keigher, W. F., 1975. Adjunctions and comonads in differential algebra, Pacific Journal of Mathematics, 59, 99-112.
• Keigher, W. F., 1997. On the ring of Hurwitz series, Communications in Algebra, 25(6), 1845-1859.
• Kim, N. K., Lee, Y., 2003. Extensions of reversible rings, Journal of Pure and Applied Algebra, 185(1-3), 207-223.
• Krempa, J., 1996. Some examples of reduced rings, Algebra Colloquium, 3(4), 289-300.
• Paykan, K., 2017. Principally quasi-Baer skew Hurwitz series rings, Bollettino dell’Unione Matematica Italiana, 10(4), 607-616.
• Rege, M. B., Chhawchharia, S., 1997. Armendariz rings, Proceedings of the Japan Academy, Ser. A, Mathematical Sciences, 73(1), 14-17.
• Yang, G., Liu, Z. K., 2008. On weak reversible rings, Taiwenese Journal of Mathematics, 12(1), 129-136.