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COMPUTABLE FIELD EMBEDDINGS AND DIFFERENCE CLOSED FIELDS: A MATHEMATICAL ANALYSIS

ABSTRACT

Computable fields are the primary focus of this paper, which contributes to the compelling field hypothesis. If the elements of a structure’s area are linked with regular numbers, then the operations that take place in this space are also computable functions. Maps between fields can be expanded to maps between their mathematical terminations, according to a variety of classical results. We’re thinking about when this will be possible. That is, should there exist a computable ex-pressure to the arithmetical terminations if the majority of the fields contained are computable and we are provided a computable guide? The classical theorems hold effectively in a computable field F if certain requirements are met, which are both important and sufficient. It’s possible to apply our findings to fields that have been shown to contain automorphisms, which are referred to as difference fields. This paper investigates how to successfully incorporate difference fields within computed difference-shut fields (these are existentially shut difference fields, to be talked about). For computable difference fields, even the most innocent resemblance to remarkable consequences fails in every way. A large range of fields (including abelian augmentations of a prime field) can be found in which the corresponding consequence can be better understood.

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