科研之友
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摘要
This paper discusses necessary and sufficient conditions on a monoid S, such that a class of left S-acts is first order axiomatisable. Such questions have previously been considered by Bulman-Fleming, Gould, Stepanova and others. %26lt;br%26gt;Let be a class of embeddings of right S-acts. A left S-act B is -flat if tensoring with B preserves the embeddings in . We find two sets (depending on a property of ) of necessary and sufficient conditions on S such that the class of all -flat left S-acts is axiomatisable. These results are similar to the %26quot;replacement tossings%26quot; results of Gould and Shaheen for S-posets. Further, we show how to axiomatise some classes using both replacement tossings and interpolation conditions, thus throwing some light on the former technique.
- 出版日期2012-10
