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Prof. Maher Shedid Mahmoud Zayed :: Publications: |
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| Title: | An application of a theorem of Rothmaler |
| Authors: | M. ZAYED; A. Y. ABDELWANIS |
| Year: | 2012 |
| Keywords: | Purely large structure, finitely accesible class, largest complete theory. |
| Journal: | Logic Journal of IGPL |
| Volume: | Not Available |
| Issue: | Not Available |
| Pages: | Not Available |
| Publisher: | Not Available |
| Local/International: | International |
| Paper Link: | Not Available |
| Full paper | Mahre shedid mahmoud zaied_Logic Jnl IGPL-2012-Zayed-jigpal_jzs003[1].pdf |
| Supplementary materials | Not Available |
| Abstract: |
In this article, the notion of purely large structure is introduced. It is shown, with the aid of a Theorem of Rothmaler, that any finitely accessible class possesses purely large structures. This applies to the class Mod(R) of all left modules over a given ring R. The theory T∗ of purely large modules is always complete. It is shown that T∗ is model-complete if and only if R is regular. For any algebra of finite representation type R, over an infinite field, T∗ is axiomatizable by one sentence over Th(Mod(R)). A characterization of pure semisimple rings, in terms of purely large modules, is obtained. |
