6 citations · 6 across the 11 of their papers we have counts for
19 papers
On the growth of Lie algebras and Jordan algebras
Be'eri Greenfeld
We prove that every increasing, polynomially bounded function is realizable, up to bi-Lipschitz equivalence, as the growth function of some finitely generated Lie algebra. This doe…
Amenability is not sensitive to the base field
Be'eri Greenfeld
We prove that the notion of amenability of a (module over) an associative algebra does not depend on the ground field, answering a question proposed by Cornulier in a MathOverflow…
On the complexity of subshifts and infinite words
Be'eri Greenfeld, Carlos Gustavo Moreira, Efim Zelmanov
We characterize the complexity functions of subshifts up to asymptotic equivalence. The complexity function of every aperiodic function is non-decreasing, submultiplicative and gro…
Noncommutative point spaces of symbolic dynamical systems
Jason P. Bell, Be'eri Greenfeld
We study point modules of monomial algebras associated with symbolic dynamical systems, parametrized by proalgebraic varieties which 'linearize' the underlying dynamical systems. F…
Rank-stability of polynomial equations
Tomer Bauer, Guy Blachar, Be'eri Greenfeld
Extending the thoroughly studied theory of group stability, we study Ulam stability type problems for associative and Lie algebras; namely, we investigate obstacles to rank-approxi…
Amenability of monomial algebras, minimal subshifts and free subalgebras
Jason P. Bell, Be'eri Greenfeld
We give a combinatorial characterization of amenability of monomial algebras and prove the existence of monomial Folner sequences, answering a question due to Ceccherini-Silberstei…
Nil algebras, Lie algebras and wreath products with intermediate and oscillating growth
Be'eri Greenfeld, Efim Zelmanov
We construct finitely generated nil algebras with prescribed growth rate. In particular, any increasing submultiplicative function is realized as the growth function of a nil algeb…
Affine Noetherian algebras, filtrations and presentations
Be'eri Greenfeld
Resco and Small gave the first example of an affine Noetherian algebra which is not finitely presented. It is shown that their algebra has no finite-dimensional filtrations whose a…
Representability of Noetherian PI-algebras
Be'eri Greenfeld, Louis Rowen
This note concerns the still open question of representability of Noetherian PI-algebras. Extending a result of Rowen and Small (with an observation of Bergman) that every finitely…
Growth of finitely generated simple Lie algebras
Be'eri Greenfeld
We realize any submultiplicative increasing function which is equivalent to a polynomial proportion of itself as the growth function of a finitely generated simple Lie algebra. As…
How do algebras grow?
Be'eri Greenfeld
We construct an increasing, submultiplicative, arbitrarily rapid function which is not equivalent to the growth function of any finitely generated algebra, demonstrating the diffic…
Generating adjoint groups
Be'eri Greenfeld
We prove two approximations of the open problem of whether the adjoint group of a non-nilpotent nil ring can be finitely generated: We show that the adjoint group of a non-nilpoten…
Chains of Semiprime and Prime Ideals in Leavitt Path Algebras
Gene Abrams, Be'eri Greenfeld, Zachary Mesyan +1
Semiprime ideals of an arbitrary Leavitt path algebra L are described in terms of their generators. This description is then used to show that the semiprime ideals form a complete…
Commuting Graphs of Boundedly Generated Semigroups
Tomer Bauer, Be'eri Greenfeld
Araújo, Kinyon and Konieczny (2011) pose several problems concerning the construction of arbitrary commuting graphs of semigroups. We observe that every star-free graph is the comm…
Growth of monomial algebras, simple rings and free subalgebras
Be'eri Greenfeld
We construct finitely generated simple algebras with prescribed growth types, which can be arbitrarily taken from a large variety of (super-polynomial) growth types. This (partiall…
Prime and Primitive Algebras with Prescribed Growth Types
Be'eri Greenfeld
Bartholdi and Smoktunowicz constructed finitely generated monomial algebras with prescribed sufficiently fast growth types. We show that their construction need not result in a pri…
Free Subalgebras of Graded Algebras
Jason P. Bell, Be'eri Greenfeld
Let be a field and let be a positively graded -algebra. We recall that is graded nilpotent if for every , the subalgebra of generat…
Affine Algebras with Arbitrary Simple Modules
Be'eri Greenfeld
We construct affine algebras with an arbitrary amount of simple modules of each dimension.
Unions of Chains of Primes
Be'eri Greenfeld, Louis H. Rowen, Uzi Vishne
The union of an ascending chain of prime ideals is not always prime. We show that this property is independent of the parallel property for semiprimes. We also show that the PI-cla…