The associated graded ring of a group ring

Solution to the presentation problem for powers of the augmentation ideal of torsion free and torsion abelian groups

“…A survey of this and important related results is found in Passi's survey article [5]. A significant impulse for the presentation of Passi and Vermani was an earlier result of Bachmann and Gruenenfelder [1].…”

“…The presentation part of the results is translated into the language of Rees rings of augmentation ideals. We do this because the Rees ring of an augmentation ideal maps canonically onto the associated graded ring of the augmentation ideal, and the associated graded ring is the construction used in [3,[5][6][7] in formulating presentation results. In Section 3, we define special NRS-generators, and show that they are linearly independent in # D n ðGÞ and D n ðGÞ: Then we define the numbers n I ðGÞ and nðGÞ and prove Theorems (1. .…”