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On the Artin-Rees Lemma for non-commutative rings

There is some discussion of this in Rowen's "Ring Theory", volume I, Section 3.5, with additional references therein. Exercise 19 on p. 462 in op. cit. states that a polycentral ideal $I$ of ...
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What is the quotient group $D^*/{F^*(1+P_D)}$ for a quaternion division algebra $D$ over a local field $F$?

To give an alternative answer, let us first recall the article "Construction of Locally Compact Near-Fields from $p$-Adic Division Algebras" by Detlef Groger: Fix a prime element $\pi_F$ of ...
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What is the quotient group $D^*/{F^*(1+P_D)}$ for a quaternion division algebra $D$ over a local field $F$?

Yes, we can.$\newcommand{\order}{\mathcal{O}}$ $\newcommand{\Z}{\mathbb{Z}}$ $\newcommand{\prim}{\mathcal{P}}$ $\newcommand{\F}{\mathbb{F}}$ First, let me remind you of the following explicit ...
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Non-vanishing criterion of the Hom space of induced representation of p-adic groups?

The main theorem of section 2.9 of Bernstein, Zelevinsky "Induced representations of reductive $p$-adic groups - I" gives a criterion for the existence of a non-zero intertwining operator ...
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