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Closure operators in modules and their characterizations
Authors: Caşu Alexei
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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
E-mail:
"Vladimir Andrunachievici"
5 Academiei str. Chisinau,
MD−2028 Moldova
E-mail:
Fulltext
– 0.38 Mb
Contents
- Commutator subgroup of Sylow 2-subgroups of alternating group and the commutator width in the wreath product
- On two stability types for a multicriteria integer linear programming problem
- Closure operators in modules and their characterizations
- On the number of topologies on countable skew fields
- New Algorithms for Finding the Limiting and Differential Matrices in Markov Chains
- Solution of the problem of the center for cubic differential systems with three affine invariant straight lines of total algebraic multiplicity four
- On self-adjoint and invertible linear relations generated by integral equations
- Loops with invariant flexibility under the isostrophy
