Homomorphisms with Semilocal Endomorphism Rings Between Modules
| Autor: | Susan F. El-Deken, Federico Campanini, Alberto Facchini |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Class (set theory)
Endomorphism Direct sum Direct-sum decomposition General Mathematics Semilocal ring Mathematics::Rings and Algebras 010102 general mathematics Dimension (graph theory) 0211 other engineering and technologies 021107 urban & regional planning 02 engineering and technology 01 natural sciences Combinatorics Morphism Module morphism Homomorphism 0101 mathematics Endomorphism ring Mathematics |
| Popis: | We study the category Morph(Mod-R) whose objects are all morphisms between two right R-modules. The behavior of the objects of Mod-R whose endomorphism ring in Morph(Mod-R) is semilocal is very similar to the behavior of modules with a semilocal endomorphism ring. For instance, direct-sum decompositions of a direct sum $\oplus _{i=1}^{n}M_{i}$ , that is, block-diagonal decompositions, where each object Mi of Morph(Mod-R) denotes a morphism $\mu _{M_{i}}\colon M_{0,i}\to M_{1,i}$ and where all the modules Mj,i have a local endomorphism ring End(Mj,i), depend on two invariants. This behavior is very similar to that of direct-sum decompositions of serial modules of finite Goldie dimension, which also depend on two invariants (monogeny class and epigeny class). When all the modules Mj,i are uniserial modules, the direct-sum decompositions (block-diagonal decompositions) of a direct-sum $\oplus _{i=1}^{n}M_{i}$ depend on four invariants. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|