An application of a theorem of Rothmaler

作者：Zayed M^*; Abdelwanis A Y

来源：Logic Journal of the IGPL, 2012, 20(6): 1214-1219.

DOI：10.1093/jigpal/jzs003

• Purely large structure
• finitely accesible class
• largest complete theory

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.

• 出版日期2012-12