On one class of modules that are close to Noetherian |
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Authors: | O Yu Dashkova |
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Institution: | 1.Department of Mathematics and Mechanics,Dnepropetrovsk National University,Dnepropetrovsk,Ukraine |
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Abstract: | We consider an R
G-module A over a commutative Noetherian ring R. Let G be a group having infinite section p-rank (or infinite 0-rank) such that C
G
(A) = 1, A/C
A
(G) is not a Noetherian R-module, but the quotient A/C
A
(H) is a Noetherian R-module for every proper subgroup H of infinite section p-rank (or infinite 0-rank, respectively). In this paper, it is proved that if G is a locally soluble group, then G is soluble. Some properties of soluble groups of this type are also obtained. |
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Keywords: | |
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