Krull-Remak-Schmidt decompositions in Hom-finite additive categories
نویسندگان
چکیده
An additive category in which each object has a Krull-Remak-Schmidt decomposition—that is, finite direct sum decomposition consisting of objects with local endomorphism rings—is known as Krull-Schmidt category. A Hom-finite is an for there commutative unital ring k, such that Hom-set length k-module. The aim this note to provide proof Krull-Schmidt, if and only it split idempotents, indecomposable ring.
منابع مشابه
Krull-schmidt Decompositions for Thick Subcategories
Following Krause [Kra99], we prove Krull-Schmidt theorems for thick subcategories of various triangulated categories: derived categories of rings, noetherian stable homotopy categories, stable module categories over Hopf algebras, and the stable homotopy category of spectra. In all these categories, it is shown that the thick ideals of small objects decompose uniquely into indecomposable thick ...
متن کاملThe Remak-Krull-Schmidt Theorem on\ Fuzzy Groups
In this paper we study a representation of a fuzzy subgroup $mu$ of a group $G$, as a product of indecomposable fuzzy subgroups called the components of $mu$. This representation is unique up to the number of components and their isomorphic copies. In the crisp group theory, this is a well-known Theorem attributed to Remak, Krull, and Schmidt. We consider the lattice of fuzzy subgroups and som...
متن کاملKrull-schmidt Categories and Projective Covers
Krull-Schmidt categories are additive categories such that each object decomposes into a finite direct sum of indecomposable objects having local endomorphism rings. We provide a self-contained introduction which is based on the concept of a projective cover.
متن کاملRefinements of chromatic towers and Krull-Schmidt decompositions in stable homotopy categories
Refinements of chromatic towers and Krull-Schmidt decompositions in stable homotopy categories
متن کاملthe remak-krull-schmidt theorem on fuzzy groups
in this paper we study a representation of a fuzzy subgroup $mu$ of a group $g$, as a product of indecomposable fuzzy subgroups called the components of $mu$. this representation is unique up to the number of components and their isomorphic copies. in the crisp group theory, this is a well-known theorem attributed to remak, krull, and schmidt. we consider the lattice of fuzzy subgroups and som...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Expositiones Mathematicae
سال: 2023
ISSN: ['1878-0792', '0723-0869']
DOI: https://doi.org/10.1016/j.exmath.2022.12.003