A Review to a Conjecture of Faith and Menal
| المصدر: | مجلة العلوم الإنسانية والتطبيقية |
|---|---|
| الناشر: | الجامعة الأسمرية الإسلامية زليتن - كليتى الآداب والعلوم |
| المؤلف الرئيسي: | Leghwel, Abd Alrzak M. (Author) |
| المجلد/العدد: | ع21 |
| محكمة: | نعم |
| الدولة: |
ليبيا |
| التاريخ الميلادي: |
2012
|
| الصفحات: | 1 - 8 |
| رقم MD: | 829070 |
| نوع المحتوى: | بحوث ومقالات |
| قواعد المعلومات: | HumanIndex |
| مواضيع: | |
| رابط المحتوى: |
| المستخلص: |
A theorem of Faith and Walker asserts that a ring R is quasi-Frobenius if and only if every injective right R-module is projective and hence that every right module over a quasi-Frobenius ring embeds in a free module. There is an open question here. If we call a ring R a right FGF-ring if every finitely generated right R-module can be embedded in a free right R-module, it is not known if the following assertion is true: The FGF- Conjecture. Every right FGF -ring is quasi-Frobenius. Here are four important results on th conjecture: (1) every left Kash , right FGF-ring is quasi-Frobenius. (2) every right self-injective, right FGF-ring is quasi Frobenius. (3) every right perfect, right FGF-ring is quasi-Frobenius. (4) ever right CS, right FGFring is quasi-Frobenius. We then turn to the fundamental work of Gomez Pardo and Guil Asensio. A ring R is called aright CF- ring if every cyclic (that is principal) right R-module can be embedded in a free module. The open question here is as follows:The CF-conjecture : every right CF-ring is right artinian . Referring to (4) from the preceding list, Gomez Pardo and Guil Asensio prove that every right CS, right CF-ring is right artinian. The paper concludes with a relation between CF-ring and CEP-ring . |
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عناصر مشابهة
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When GP - injective Rings are P - injective : A Report on A Problem
بواسطة: Leghwel, Abd Alrzak M. منشور: (2009) -
A Note on E-Self-Projective Modules
بواسطة: Leghwel, Abd Alrzak منشور: (2009) -
On The Excess of Hadamard Matrix
بواسطة: Leghwel, Abd Alrzak M. منشور: (2011) -
A Remark on the Hadamard Matrices of the Williamson Type
بواسطة: Leghwel, Abd Alrzak M. منشور: (2014) -
On Some Applications of Hadamard Matrices
بواسطة: Leghwel, Abd Alrzak M. منشور: (2012)
