On the Extensions of Zassenhaus Lemma and Goursat’s Lemma to Algebraic Structures

Fanning Meng, Junhui Guo and Li Guo

Journal of Mathematics, 2022, vol. 2022, 1-10

Abstract: The Jordan–Hölder theorem is proved by using Zassenhaus lemma which is a generalization of the Second Isomorphism Theorem for groups. Goursat’s lemma is a generalization of Zassenhaus lemma, it is an algebraic theorem for characterizing subgroups of the direct product of two groups G1×G2, and it involves isomorphisms between quotient groups of subgroups of G1 and G2. In this paper, we first extend Goursat’s lemma to R-algebras, i.e., give the version of Goursat’s lemma for algebras, and then generalize Zassenhaus lemma to rings, R-modules, and R-algebras by using the corresponding Goursat’s lemma, i.e., give the versions of Zassenhaus lemma for rings, R-modules, and R-algebras, respectively.

Date: 2022
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jmath/2022/7705500.pdf (application/pdf)
http://downloads.hindawi.com/journals/jmath/2022/7705500.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:7705500

DOI: 10.1155/2022/7705500

Access Statistics for this article

More articles in Journal of Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().