Research Notes:
Keats-Rohan states, [1]
Willelm Peurel De Nottingeham
Norman, major tenant-in-chief centred upon Nottinghamshire and Derbyshire. … Founder of the priory of St James at Northampton, and of Lenton priory, Nottinghamshire, a cell of Cluny, his foundateion charter mentioned his brother Robert. By his wife Adleine he had issue two sons named William, of whom one predeceased hims, and a daughter Adeliz who married Richard I de Redvers. He died on 28 January 1113/14 according to an obituary of St James, Northampton (BL Cotton Tiberius E. v, fol. 1v). According to the same obiturary his wife predeceased him, but in fact she occurs as the mother of his successor William II Peverel in the 1129/30 Pipe Roll.
[1] K. S. B. Keats-Rohan, Domesday People, A Prosopography of persons occurring in English documents, 1066-1166 (Boydell & Brewer Ltd, 1999), 494, [GoogleBooks].