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On Minimax and Related Modules

Published online by Cambridge University Press:  20 November 2018

Peter Rudlof
Peter Rudlof*
Affiliation:
Mathematisches Institut der Universität, Theresienstr. 39, D 8000 München 2, Federal Republic of Germany
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Abstract

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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).

Keywords

13E0513C05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 1 , 01 December 1991 , pp. 154 - 166
Copyright
Copyright © Canadian Mathematical Society 1989

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