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Large and Infinite Nearrings

Computations with infinite nearrings inevitably lead to undecidable problems. In practice, the same is already true for finite nearrings of sizes above . Currently, only d.g. nearrings of that size can be handled properly. On the other hand, quite a lot can be done with finitely generated rings, and there is hope to save a reasonable portion of computability to other special types of infinite nearrings, such as polynomial nearrings ([22]), even bigger d.g. nearrings ([21]), nearrings generated by one element, and others. Some first results concerning this are contained in [11]. Also, even partial solutions such as semialgorithmic, probabilistic, or approximative methods are of high value for the solution of many problems. There is already some experience in computing with such objects ([9], [10]).

Juergen Ecker
Wed May 13 09:13:56 CEST 1998