A Note On Clean Abelian Groups

Brendan Goldsmith; P. Vamos

doi:10.21427/kgn6-jk47

A Note On Clean Abelian Groups

Brendan Goldsmith, P. Vamos

Technological University Dublin

Research output: Contribution to journal › Article › peer-review

Abstract

Nicholson defined a ring to be clean if every element is the sum of a unit and an idempotent. A module is clean if its endomorphism algebra is clean. We show that torsion-complete Abelian p-groups are clean and characterize the clean groups among the class of totally projective p-groups. An example is given of a clean p-group which is neither totally projective nor torsion- complete

Original language	English
Pages (from-to)	181-191
Number of pages	11
Journal	Rendiconti del Seminario Matematico della Universita di Padova
Volume	117
DOIs	https://doi.org/10.21427/kgn6-jk47
Publication status	Published - 1 Jan 2007

Keywords

clean
abelian groups
torsion-complete
totally projective
p-groups

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10.21427/kgn6-jk47Licence: CC BY-NC

Cite this

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AB - Nicholson defined a ring to be clean if every element is the sum of a unit and an idempotent. A module is clean if its endomorphism algebra is clean. We show that torsion-complete Abelian p-groups are clean and characterize the clean groups among the class of totally projective p-groups. An example is given of a clean p-group which is neither totally projective nor torsion- complete

KW - clean

KW - abelian groups

KW - torsion-complete

KW - totally projective

KW - p-groups

UR - https://www.scopus.com/pages/publications/84878224148

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DO - 10.21427/kgn6-jk47

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JO - Rendiconti del Seminario Matematico della Universita di Padova

JF - Rendiconti del Seminario Matematico della Universita di Padova

ER -

A Note On Clean Abelian Groups

Abstract

Keywords

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