Geodesic
On Minimax and Related Modules
Canadian journal of mathematics, Tome 44 (1991) no. 1, pp. 154-166

Voir la notice de l'article provenant de la source Cambridge University Press

A module M is called a minimax module, if it has a finitely generated submodule U such that M/U is Artinian. This paper investigates minimax modules and some generalized classes over commutative Noetherian rings. One of our main results is: M is minimax iff every decomposition of a homomorphic image of M is finite.From this we deduce that:- All couniform modules are minimax.- All modules of finite codimension are minimax.- Essential covers of minimax modules are minimax. With the aid of these corollaries we completely determine the structure of couniform modules and modules of finite codimension.We then examine the following variants of the minimax property:- replace U “ finitely generated” by U “ coatomic” (i.e. every proper submodule of U is contained in a maximal submodule);- replace M/U “ Artinian” by M/U “ semi-Artinian” (i.e. every proper submodule of M/U contains a minimal submodule).
DOI : 10.4153/CJM-1992-009-7
Mots-clés : 13E05, 13C05 
Rudlof, Peter. On Minimax and Related Modules. Canadian journal of mathematics, Tome 44 (1991) no. 1, pp. 154-166. doi: 10.4153/CJM-1992-009-7
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