The Ring of Tomrair  - the Royal Emblem of the Ui Imair Kings in Dublin

The Irish chroniclers referred to the Ring of Tomrair and Sword of Carlus as the royal emblems of the Ui Imair kings in Dublin. The Ring of Tomrair bore the name of a tanist,  meaning the son and heir of the king of Lochlann in the mid-ninth century.

Tomrair was a high-ranking jarl in the Viking Age as the son and heir of the king of Lochlann. He commanded a fleet that attacked the monasteries and Gaelic settlements of County Kildare in 848.

Lorcán mac Laigin, King of Leinster, and his ally, Ólchobar mac Cináeda, King of Munster, fought Tomrair and his army at the Battle of Sciath Nechtain in 848. Jarl Tomrair and twelve hundred Viking warriors died on the battlefield. 

Historians suspect Tomrair was the tanist, or the son and heir, of Godfraid, King of Lochlann. 

The kingdom of Lochlann encompassed the Norse colonies in Scotland and the Isle of Man. Tomrair may have been the brother of “Amlaíb, son of the king of Lochlann”, or Olaf the White.

Amlaíb Conung, or Olaf the White, was active in the Irish Sea region in the mid-ninth century. He arrived in Ireland with a Viking fleet and expelled the Danes from the longphort at Áth Cliath, or Dublin in 853. 

The Irish chroniclers recounted Amlaíb Conung, or Olaf the White, proclaimed himself king of all the Vikings in Ireland. He shared the kingship of Dublin with his brothers, Imar or Ivar the Boneless and Auisle.

Amlaíb Conung and Imar ruled over the Scandinavian colonists from their stronghold in Dublin for the next twenty years. Imar or Ivar the Boneless founded the Ui Imair dynasty in Dublin.

The Ui Imair kings deemed the arm-ring of Tomrair a sacred object. The Ring of Tomrair and the Sword of Carlus formed the royal emblems of the Hiberno-Scandinavian kings of Dublin.

The Vikings kept the Ring of Tomrair in a temple in Dublin. A pagan priest wore the Ring of Tomriair during rituals to Thor. 

The Vikings in Dublin traditionally swore oaths on the Ring of Tomrair.

The Annals of the Fours Masters claimed Máel Sechnaill mac Domnaill, the High of Ireland, took possession of the Ring of Tomrair and Sword of Carlus when he captured Dublin in 995.

Scholars believed the Hiberno-Scandinavian kings of Dublin revered the Ring of Tomrair to honour a jarl of the same name. 

The Viking kings of Dublin, Olaf and Ivar, esteemed the ring in memory of the warrior hero, Tomrair. 

The poets of Ireland spoke of the Vikings in Dublin as the "race of Tomar" and "Tomar's nobles". 

The early Viking history of Ireland is discussed in:

Olaf the White and Ivar the Boneless - The Viking Kings of Dublin: https://www.amazon.com/dp/B0916GJ3B2

And Vikings in Ireland (870 - 914): https://www.amazon.com/dp/B096KVNBZK

References

 Wikipedia - Tomrair: https://en.wikipedia.org/wiki/Tomrair Viking Kings of Britain and Ireland: The Dynasty of Ivarr to A.D. 1014 By Clare Downham: https://books.google.ie/books?id=_1hwDwAAQBAJ&pg=PT63... Wikipedia - Lorcán mac Cellaig: https://en.wikipedia.org/wiki/Lorc%C3%A1n_mac_Cellaig Wikipedia - Gofraid of Lochlann: https://en.wikipedia.org/wiki/Gofraid_of_Lochlann UCC - Annals of Ulster: https://celt.ucc.ie//published/T100001A/index.html