Some applications of zorn's lemma in algebra

D.D. Anderson; D.E. Dobbs; M. Zafrullah

doi:10.5556/j.tkjm.40.2009.463

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Some applications of zorn's lemma in algebra

Journal article

Open access

Peer reviewed

Some applications of zorn's lemma in algebra

D.D. Anderson, D.E. Dobbs and M. Zafrullah

Tamkang Journal of Mathematics, Vol.40(2), pp.139-150

2009

DOI: 10.5556/j.tkjm.40.2009.463

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Abstract

We indicate some new applications of Zorn's Lemma to a number of algebraic areas. Specifically, we show that a property P holds for all the subobjects of a given object if and only if P supports both the chain condition from Zorn's Lemma and some finitistic conditions on subobjects that have the flavor of mathematical induction. The specific algebraic contexts considered are modules, sets, groups, algebras, and integral domains. Particular emphasis is given to applications involving star operations on integral domains.

Finitely generated

Flat

Going-down

Going-up

Injective

Integral domain

Krull domain

Projective

Prüfer domain

Semisimple

Star operation

Subalgebra

Subgroup

Submodule

Suboboject

Zorn's Lemma

Details

Title: Subtitle: Some applications of zorn's lemma in algebra
Creators: D.D. Anderson
D.E. Dobbs
M. Zafrullah
Resource Type: Journal article
Publication Details: Tamkang Journal of Mathematics, Vol.40(2), pp.139-150
DOI: 10.5556/j.tkjm.40.2009.463
ISSN: 0049-2930
Publisher: Tamkang University
Language: English
Date published: 2009
Academic Unit: Mathematics
Record Identifier: 9984230626802771

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