<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2023-04-13</periodOfReport>

    <noSecuritiesOwned>1</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001579241</issuerCik>
        <issuerName>Allegion plc</issuerName>
        <issuerTradingSymbol>ALLE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001938899</rptOwnerCik>
            <rptOwnerName>Rubin Ellen</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O SCHLAGE LOCK COMPANY LLC</rptOwnerStreet1>
            <rptOwnerStreet2>11819 N. PENNSYLVANIA STREET</rptOwnerStreet2>
            <rptOwnerCity>CARMEL</rptOwnerCity>
            <rptOwnerState>IN</rptOwnerState>
            <rptOwnerZipCode>46032</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
        </reportingOwnerRelationship>
    </reportingOwner>

    <footnotes></footnotes>

    <remarks>Exhibit 24 - Power of Attorney is attached.</remarks>

    <ownerSignature>
        <signatureName>/s/ Eric Gunning, Attorney-In-Fact</signatureName>
        <signatureDate>2023-04-17</signatureDate>
    </ownerSignature>
</ownershipDocument>
