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Noncontrolling Interest (Details)	Sep. 30, 2023	Sep. 30, 2022
TCI
Noncontrolling Interest [Line Items]
Ownership interest	78.40%
IOR
Noncontrolling Interest [Line Items]
Ownership interest	81.10%	81.10%

X

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

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X

- Definition

The parent entity's interest in net assets of the subsidiary, expressed as a percentage.

+ References

No definition available.

+ Details

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X

- Details

Name:	srt_OwnershipAxis=arl_TranscontinentalRealtyInvestorsIncMember
Namespace Prefix:
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Balance Type:
Period Type:

X

- Details

Name:	srt_OwnershipAxis=arl_IncomeOpportunityRealtyInvestorsIncMember
Namespace Prefix:
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Balance Type:
Period Type: