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On maximal chains in the lattice of module topologies. (Russian, English) Zbl 1020.16033
Sib. Mat. Zh. 42, No. 3, 491-506 (2001); translation in Sib. Math. J. 42, No. 3, 415-427 (2001).
Let $$(R,\tau_R)$$ be a separated topological unital ring and let $$M$$ be a left unitary $$R$$-module. The article is devoted to the following questions: 1. Does $$M$$ admit an $$n$$-premaximal $$(R,\tau_R)$$-module topology (for the definition, see the authors’ paper [Izv. Akad. Nauk Respub. Mold., Mat. 1996, No. 1, 96-105 (1996)]) for each natural number $$n$$? 2. How do the $$n$$-premaximal topologies on $$M$$ look like if they exist?
The authors indicate conditions under which the question of existence of premaximal topologies has a positive solution and has a negative solution. They describe $$n$$-premaximal topologies in the case when $$R$$ is a skew field and the topology $$\tau_R$$ is determined by a real absolute value.

##### MSC:
 16W80 Topological and ordered rings and modules 54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
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