15,789 reputation
23594
bio website sci.ccny.cuny.edu/~benjamin
location New York City
age 42
visits member for 3 years, 11 months
seen 17 mins ago

I am an algebraist interested in a broad range of areas. I've worked on semigroups, geometric group theory, algebraic combinatorics, representation theory, self-similar groups (aka automaton groups), profinite groups and random walks on semigroups and groups. I've been particularly interested in interactions between these areas and Computer Science and am fond of algorithmic questions. I've also dabbled with operator algebras associated to etale groupoids and inverse semigroups. Currently, I am interested in applications of finite semigroup theory to finite state Markov chains.

My blog is http://bensteinberg.wordpress.com/author/bsteinbg/


2h
comment Idempotent ideal in ring of continuous functions
Continuous functions on what space? If your space is totally disconnected there can be lots of idempotents
6h
comment Are monoids with zero and partial homomorphisms related?
I mean if f(a) and f(b) and f(ab) are defined then they are equal.
10h
comment Are monoids with zero and partial homomorphisms related?
I don't require the domain of a partial homomorphism be the whole semigroup. I think one should allow the most lax notion of partial. Equality should only be required when everything is defined
1d
comment John Nash's Mathematical Legacy
I flagged for CW so that we can upvote. I am sorry to hear the news
1d
comment Earliest source for a Lie algebra construction
Making a new semigroup or of an old one by fixing an element x and mapping (a,b) to axb is called a variant and has been around since probably the 50s or sixties.
1d
answered Are monoids with zero and partial homomorphisms related?
2d
comment On sentences true in all finite groups
@JoelDavidHamkins, I am not sure whether it can be recoded
2d
comment On sentences true in all finite groups
cmi.univ-mrs.fr/~coulbois/articles/equation.pdf gives an equation which has a solution in all finite groups but not in the free group.
May
22
comment Different ways of having infinite global dimension
I think you can find such examples by googling but from what I read it is unknown if there is a ring which is both left and right noetherian whose simple modules all have finite projective dimension but who has infinite global dimension
May
22
revised Different ways of having infinite global dimension
added 211 characters in body
May
22
comment Different ways of having infinite global dimension
Let me think. But in any event this shows that if your hypothesis is true then all cyclic modules have finite projective dimension and your direct sum condition doesn't help. So what you really want is an example where each cyclic module has finite projective dimension which is unbounded.
May
21
comment pseudovarieties and profinite group : do * and g() commute?
@user182085, By the way it is usual to accept an answer when somebody gives one.
May
21
comment Different ways of having infinite global dimension
Sometimes we miss something simple.
May
21
comment Different ways of having infinite global dimension
By the way for Artinian rings the global dimension is always carried by simples.
May
21
revised Different ways of having infinite global dimension
added 274 characters in body
May
21
comment Different ways of having infinite global dimension
Since Ext commutes with direct sums you get that a summand in a finite direct sun of modules of finite projective dimension has finite projective dimension.
May
21
comment Different ways of having infinite global dimension
If a cyclic R-modules is a retract of a direct sum then it is a retract of a finite direct sum because the splitting takes the generator into finitely many of the summands.
May
21
answered Different ways of having infinite global dimension
May
21
comment Different ways of having infinite global dimension
I seem to vaguely recall that by a result of Auslander the global dimension is the sup of the projective dimensions of all cyclic R-modules. This would imply what you want can't happen if I am recalling correctly
May
18
reviewed No Action Needed Counting ways to Arrange Variable Sized Objects into Fixed Number of Spaces