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Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.
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How to detect if an element in a completed group algebra is a unit?
Completed group algebras appear in Iwasawa theory and in many situations you want to know if an element is a unit. For example consider $K_n=\mathbb{Q}(\mu_{p^n})$ and $G=\varprojlim \mathrm{Gal}(K_n/ …