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Article
On m-Regular Rings

Authors: Zubayda M. Ibraheem --- Maha F. Khalaf
Journal: AL-Rafidain Journal of Computer Sciences and Mathematics مجلة الرافدين لعلوم الحاسوب والرياضيات ISSN: 18154816 Year: 2012 Volume: 9 Issue: 2 Pages: 61-70
Publisher: Mosul University جامعة الموصل

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Abstract

As a generalization of regular rings, we introduce the notion, of m-regular rings, that is for all , there is a fixed positive integer m such that is a Von-Neumann regular element. Some characterization and basic properties of these rings will be given. Also, we study the relation-ship between them and Von-Neumann regular rings, -regular rings, reduced rings, locally rings, uniform rings and 2-primal rings.

كتعميم للحلقات المنتظمة, قدمنا الحلقات المنتظمة من النمط -m على أنها لكل يوجد عدد صحيح موجب ثابت m بحيث أن يكون منتظم. في هذا البحث درسنا المميزات والخواص الأساسية له وكذلك العلاقة بين الحلقات المنتظمة من النمط - m والحلقات المنتظمة من النمط - , والحلقات المختزلة والحلقات المحلية والحلقات الموحدة.


Article
On Almost WJCP-Injective Rings

Authors: R.D. Mahmood --- Sh.H. Ahmad
Journal: JOURNAL OF EDUCATION AND SCIENCE مجلة التربية والعلم ISSN: 1812125X Year: 2019 Volume: 28 Issue: 1 Pages: 83-89
Publisher: Mosul University جامعة الموصل

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Abstract

Let R be a ring. The ring R is called right almost WJCP-injective. If for any b∉Y(R), (right non singular) there exists a left ideal X_b of R such that l_R r_R (b)=Rb⊕X_b. In this paper, we give some characterization and properties of almost WJCP-injective rings, which are proper generalization of JCP-injective ring and almost AP-injective ring. Then, we study the regularity of the right almost WJCP-injective ring and some important results which are known for the right JCP-injective rings to be hold for the right almost WJCP-injective rings.

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