# ra.rings-and-algebras's questions - English 1answer

1.928 ra.rings-and-algebras questions.

### Unitary element of the group algebra

Let $G$ be a torsion free group. Are unitary elements of $\mathbb CG$ studied? By unitary element I mean an element $\alpha$ in $\mathbb CG$, such that $\alpha^*\alpha=1$? Do the triviality of unitary ...

### 4 Does this element belong to $\mathbb CG$?

Let $G$ be a torsion-free group. Let $\alpha$ be a symmetric element of $\mathbb CG$, i.e. $\alpha^*=\alpha$, with $\|\alpha\|_1=\sum|\alpha(g)|<1$, so $\beta:=\sum_{n\ge 0}(-1)^n\alpha^n$ is an ...

### 5 Duality between coalgebras and (pseudocompact) algebras - uniqueness

The following result is well-known. It can for example be found in [Iovanov: The representation theory of profinite algebras, Theorem 1.0.2]. For definitions, see below. Let $k$ be a field. The ...

### 4 Values attained by the coheight of $(H \setminus H^\times)^k$ as a function of $H$ and $k$

Edit (Apr 24, 2017). I'm updating this post in the light of the latest developments of a related thread. Let $H$ be a multiplicatively written, commutative monoid, and set $M := H \setminus H^\times$,...

### Question about Jacobson rings

I am studying theorem (1.11)* from this article: https://sci-hub.tw/https://onlinelibrary.wiley.com/doi/abs/10.1112/jlms/s2-9.2.337 Theorem (1.11)*. Let $R$ be a Jacobson ring, then $S = R[x,\alpha]$ ...

### -4 Maximal subring of matrix ring [closed]

0 answers, 50 views ra.rings-and-algebras
Which ring is the maximal subring of matrix ring $M_{n}\left(R\right)$.n is the given number,maximal subring means maximal dimension.

### 5 Equivalence of idempotents and projective modules over nonunital rings

1 answers, 96 views ra.rings-and-algebras modules
For a nonunital ring $R$ (or "rng") one has to be a little bit careful when considering the category of (left or right) $R$-module and, furthermore, the standard equivalent definitions of projective ...

### 3 Can we abelianize quasi-isomorphisms of dga?

Suppose that $A \leftarrow X_1 \to \dots \leftarrow X_m \to B$ is quiso of differential graded algebras, and $A, B$ happen to be (graded) commutative. Can we find commutative $Y_1, \dots, Y_n$ ...

### Cassels Frohlich, Module index

In the book â€śAlgebraic Number Theoryâ€ť written by Cassels and Frohlich, module index is defined. Let R be Dedekind domain, K be its quotient field, U be a n-dimensional vector space over K, and L,M be ...

### 4 Commutators for quantum Lie algebras

Can the usual definition of a Lie algebra via commutators be simply adapted to quantum Lie algebras? Graphically you have the IHX scheme, with the X being a virtual crossing (so to say). Does it ...

### 2 Homological conjecture for finite dimensional algebras

In the theory of finite dimensional algebras there are many homological conjectures. When working over an algebraically closed field it is well known that any such algebra is Morita equivalent to a ...

### 11 Group rings such that every (countably generated) module has a maximal submodule

Every (non-zero) finitely generated module over a ring has a maximal proper submodule by a simple application of Zorn's lemma. I am interested in the following question, with two variants. ...