UNIQUENESS OF DECOMPOSITION, FACTORISATIONS, G-GROUPS AND POLYNOMIALS

Authors : Alberto FACCHİNİ, Serap SAHİNKAYA

Pages : 107-128

Doi:10.24330/ieja.440235

View : 14 | Download : 13

Publication Date : 2018-07-05

Article Type : Research Paper

Abstract :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.
Keywords : Krull Schmidt Theorem, indecomposable module, direct sum decomposition, endomorphism ring, uniserial module