Topological Ordered Rings and Measures
Francisco Javier García‐Pacheco, M. A. Moreno-Frías, Marina Murillo‐Arcila · Results in Mathematics · 2023
Abstract Given a ring endowed with a ring order, we provide sufficient conditions for the order topology induced by the ring order to become a ring topology (analogous results for module orders are consequently derived). Finally, the notions of Radon and regular measures are transported to the scope of module-valued measures through module orders. Classical characterizations of these measures are obtained as well as the hereditariness of regularity for conditional ring-valued measures.