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Document type

Bachelor thesis

Publication date

2022-01-24

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cc-by-nc-nd (c) Guillem Sedó i Torres, 2022
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/186862

Decomposition theorems of modules over commutative rings

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Abstract

[en] The Fundamental Theorem of Finitely Generated Abelian Groups is a very important result that allows us to describe explicitly the finitely generated abelian groups. This theorem can naturally be generalized to finitely generated modules over principal ideal domains. The difficulty arises when we try to extend it to other types of rings. In this work we prove a generalization of this, the decomposition theorem of finitely generated modules over Dedekind domains. We also explore other similar decomposition and we characterize the rings such that all their modules have a decomposition of simple and cyclic modules.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Santiago Zarzuela

Subject

Grups abelians, Treballs de fi de grau, Anells commutatius, Àlgebra commutativa

Subject (English)

Abelian groups, Bachelor's theses, Commutative rings, Commutative algebra

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

SEDÓ I TORRES, Guillem. Decomposition theorems of modules over commutative rings. [consulted: 16 of August of 2026]. Available at: https://hdl.handle.net/2445/186862

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