Indecomposible division algebras of prime exponent.
In this paper we present a method of obtaining new examples of spaces of orderings by considering quotient structures of the space of orderings - it is, in general, nontrivial to determine whether, for a subgroup the derived quotient structure is a space of orderings, and we provide some insights into this problem. In particular, we show that if a quotient structure arising from a subgroup of index 2 is a space of orderings, then it necessarily is a profinite one.
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