Mariano Suárez-Alvarez
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Jun
29
answered Find the necessary and sufficient condition for $A^m\to0$
Jun
29
comment Example of non isomorphic groups with isomorphic group algebras
You can use any invariant of a group algebra to show that two group algebras are not isomorphic, in characteristic zero or not. For example, the number of conjugacy classes is an invariant of the algebra, the number of 1-dimensional representations, etc. In general, your question »I was wondering if there is some field\dots» one cannot say much more that this.
Jun
28
comment Proving that the cross ratio is a Möbius transformation
The determinant of a two by two matriz is zero iff its two columns are linearly dependent.
Jun
28
comment Global dimension of an intermediate ring
You are interested in commutative rings, and my rings are usually non-commutative. A good reference is the book by McConnell and Robson, which has a whole chapter on gldim.
Jun
28
comment Group $G$ whose center $Z(G)$ is cyclic and with $G/Z(G)$ commutative
Nice question. ${}$
Jun
28
comment Global dimension of an intermediate ring
If $R\subseteq S$ are commutative rings and $R$ is a direct summanf of $S$ as an $R$-module, then the global dimension of $R$ is at most the global dimension of $S$ plus the projective dimension of $S$ over $R$. There are several such results (but I do not recall any in which you start with a ring sandwiched between two other rings) You can also use the weaker condition that $S$ be faithfully flat over $R$ plus something else and such things
Jun
28
comment Global dimension of an intermediate ring
I created a new tag for global-dimension; there are many existing questions to which it applies.
Jun
28
revised Global dimension of an intermediate ring
edited tags
Jun
28
comment Global dimension of an intermediate ring
The global dimension is very fragile :-)
Jun
28
answered Global dimension of an intermediate ring
Jun
28
comment Why is this language not regular?
Please include the description of the language in your question.
Jun
27
comment Is a nontrivial finite group of order $n$ always isomorphic to a subgroup of $GL_{n-1}(\mathbb{Z})$?
@user135520, yes.
Jun
27
answered Is a nontrivial finite group of order $n$ always isomorphic to a subgroup of $GL_{n-1}(\mathbb{Z})$?
Jun
27
comment Is a nontrivial finite group of order $n$ always isomorphic to a subgroup of $GL_{n-1}(\mathbb{Z})$?
I've undeleted this to observe that the argument is wrong: left multiplication by an element $g\neq1$ most certainly does not fix the identity element!
Jun
27
comment Prove that there are infinity many tautologies.
Apart from that, and as usual, you have managed to write something that is entirely opaque to me!
Jun
27
comment Prove that there are infinity many tautologies.
Every set of finite strings has one of minimal length.
Jun
27
comment Prove that there are infinity many tautologies.
@DougSpoonwood, my proof also does not work if what you wanted to do was chocolate cookies.
Jun
27
comment Is the supremum norm the only $ C^{*} $-norm on $ {C_{c}}(X) $, equipped with the usual pointwise operations?
The norm on a C*-álgebra is determined by the algebra structure, no?
Jun
27
comment Continuous action on tensor product
No, I am randomly mentioning it... :P
Jun
27
comment Prove that there are infinity many tautologies.
Why do you think you are supposed to do a proof by contradiction?