Triangular matrix representation of skew Hurwitz series rings

Subject Areas : Algebra

Kamal Paykan ¹ , Abasalt Bodaghi ²

1 - Department of Basic Sciences, Garmsar Branch, Islamic Azad University, Garmsar, Iran
2 - Department of Mathematics, Garmsar Branch, Islamic Azad University, Garmsar, Iran

Received: 2021-08-28 Accepted : 2022-11-30 Published : 2024-07-06

Keywords: نمایش ماتریس مثلثی کامل تعمیم یافته, بعد مثلثی, حلقه سری های هرویتس اریب, حلقه PWP,

Abstract :

. A ring R is a Baer ring if the right annihilator of every nonempty subset of R is generated by an idempotent. Moreover, R is called quasi-Baer if the right annihilator of every right ideal of R is generated as a right ideal by an idempotent. The piecewise prime ring (simply, PWP ring) is a quasi-Baer ring with finite triangulating dimension. Birkenmeier and Park raised the open problems to enlarge the class of ring extensions of PWP rings which are also PWP rings and to enlarge the class of ring extensions of rings with finite triangulating dimension which also have finite triangulating dimension. In this paper, we enlarge the class of ring extensions of PWP rings. In particular, we investigate the problem when a skew Hurwitz series ring (HR,α) has the same triangulating dimension as the ring R, where R is a ring equipped with an endomorphism α. Furthermore, for a piecewise prime ring we determine a large class of the skew Hurwitz series ring which have a generalized triangular matrix representation for which the diagonal rings are prime.

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