On Extensions of Injectivity of Graded Modules
Hesham Sherif El-Sayed Hussein;
Abstract
This thesis has two predominant objectives. On one hand, we investigate
the relation between the concept of graded essential extensions and
graded injectivity of graded modules. Actually, a characterization of the
graded injective hull in terms of graded essential extensions is deduced and
graded versions of (Echman-Schopf) theorem and (Papp-Bass) theorem has
been proved. On the other hand, we study one of the most important extensions
of graded injectivity, namely the graded soc-injectivity. Roughly
speaking, after de ning the graded soc-injectivity of graded modules we
provide characterizations of semiartinian graded rings, graded noetherian
rings, and graded quasi-Frobenius rings in terms of graded soc-injectivity.
1
the relation between the concept of graded essential extensions and
graded injectivity of graded modules. Actually, a characterization of the
graded injective hull in terms of graded essential extensions is deduced and
graded versions of (Echman-Schopf) theorem and (Papp-Bass) theorem has
been proved. On the other hand, we study one of the most important extensions
of graded injectivity, namely the graded soc-injectivity. Roughly
speaking, after de ning the graded soc-injectivity of graded modules we
provide characterizations of semiartinian graded rings, graded noetherian
rings, and graded quasi-Frobenius rings in terms of graded soc-injectivity.
1
Other data
| Title | On Extensions of Injectivity of Graded Modules | Other Titles | عن إمتدادات الحقن للتشكيلات المدرجة | Authors | Hesham Sherif El-Sayed Hussein | Issue Date | 2015 |
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