A division ring is a ring (see Chapter Rings) in which every non-zero element has an inverse. The most important class of division rings are the commutative ones, which are called fields.
GAP supports finite fields (see Chapter Finite Fields) and abelian number fields (see Chapter Abelian Number Fields), in particular the field of rationals (see Chapter Rational Numbers).
This chapter describes the general GAP functions for fields and division rings.
If a field F is a subfield of a commutative ring C, C can be considered as a vector space over the (left) acting domain F (see Chapter Vector Spaces). In this situation, we call F the field of definition of C.
Each field in GAP is represented as a vector space over a subfield
(see IsField), thus each field is in fact a field extension in a
natural way, which is used by functions such as Norm and Trace
(see Galois Action).
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GAP 4 manual