Fans in the theory of real semigroups
Volume 556 / 2020
Dissertationes Mathematicae 556 (2020), 1-79
MSC: 06F25, 11E81, 14P10, 20M25.
DOI: 10.4064/dm819-6-2020
Published online: 26 October 2020
Abstract
In [DP1] we introduced the notion of a real semigroup (RS) as an axiomatic framework to study diagonal quadratic forms with arbitrary entries over (commutative, unitary) semireal rings. Two important classes of RSs were studied at length in [DP2], [DP3]. In this paper we introduce and develop the theory of RS-fans, a third class of RSs providing a vast generalization of homonymous notions previously existing in field theory and in the theories of abstract order spaces and of reduced special groups. The Introduction briefly reviews the existing theories of fans and describes the contents of the paper.
