Direct products of modules whose endomorphism rings have at most two maximal ideals

In this article, we present the classical Krull-Schmidt Theorem for groups, its statement for modules due to Azumaya, and much more modern variations on the theme, like the so-called weak Krull-Schmidt Theorem, which holds for some particular classes of modules. Also, direct product of modules is considered. We present some properties of the category of G-groups, a category in which Remak's results about the Krull-Schmidt Theorem for groups can be better understood. In the last section, direct-sum decompositions and factorisations in other algebraic structures are considered.

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Direct products of modules whose endomorphism rings have at most two maximal ideals

Abstract: Monogeny classes and epigeny classes have proved to be useful in the study of direct sums of uniserial modules and other classes of modules. In this paper, we show that they also turn out to be useful in the study of direct products.

Cited by 2 publications

References 21 publications

Some natural additive decompositions of elements in bimodules

Some natural additive decompositions of elements in bimodules

Uniqueness of Decomposition, Factorisations, G-Groups and Polynomials

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