A uniserial module over a valuation domain R is non-standard if it is not isomorphic to J I, where I ≤ J are submodules of the field of quotients Q of R. This paper gives a complete answer to the following question: under which conditions is a quotient of a non-standard uniserial R-module still non-standard? Examples are given of the different possibilities, using constructions of non-standard uniserial modules, which depend on the diamond principle. © 1990.
On non-standard uniserial modules over valuation domains and their quotients
BAZZONI, SILVANA;
1990
Abstract
A uniserial module over a valuation domain R is non-standard if it is not isomorphic to J I, where I ≤ J are submodules of the field of quotients Q of R. This paper gives a complete answer to the following question: under which conditions is a quotient of a non-standard uniserial R-module still non-standard? Examples are given of the different possibilities, using constructions of non-standard uniserial modules, which depend on the diamond principle. © 1990.File in questo prodotto:
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