Authors: Caşu Alexei
Abstract
This work is dedicated to the investigation of closure operators
of a module category $R$-Mod. The principal types of closure operators of $R$-Mod
are studied and their characterizations are indicated, using dense or (and) closed
submodules. The method of description of the closure operators consists in the
elucidation of properties of functions which separate in every module, the
set of dense submodules and the set of closed submodules.
The main properties of the closure operators of $R$-Mod are studied:
weakly heredity~{--} idempotency, maximality~{--} minimality, heredity~{--} coheredity,
as well as diverse combinations of them. Altogether, 16 types of the closure operators
are described, among which 7 types possess double characterizations (by dense submodules and by
closed ones).
Institute of Mathematics and Computer Science
"Vladimir Andrunachievici"
5 Academiei str. Chisinau,
MD−2028 Moldova
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