The aim of this expository article is to discuss the μ-invariant associated to finitely generated modules over Iwasawa algebras. This is an important invariant which was first discovered by Iwasawa in the 1960’s and occurs in his seminal work on cyclotomic fields [9], [10]. In fact, Iwasawa conjectured that his μ-invariant was always zero for the pprimary subgroup of the ideal class group of th...

Let R be a complete discrete valuation ring, S = R[[u]] and d a positive integer. The aim of this paper is to explain how to compute efficiently usual operations such as sum and intersection of sub-S-modules of S. As S is not principal, it is not possible to have a uniform bound on the number of generators of the modules resulting from these operations. We explain how to mitigate this problem, ...