The next meeting of the Algebra and Logic Seminar will be held
on June 1, 2018 (Friday) at 1 p.m. in Room 578 of the Institute of Mathematics and Informatics.
A talk on
ON THE NILPOTENCY INDEX OF NIL ALGEBRAS
will be delivered by
Matyas DOMOKOS (Renyi Institute, Budapest).
Abstract. Kaplansky proved in 1946 that finitely generated associative nil algebras (over an infinite base field) of bounded nil index are nilpotent. For positive integers n and m (and a fixed infinite base field) denote by d(n,m) the minimal positive integer d such that any nil algebra R generated by m elements and having bounded nil index n is nilpotent of nilpotency degree d.
Recent results of Derksen and Makam on generators of rings of matrix invariants together with a theorem of Zubkov from 1996 yield an explicit upper bound on d(n,m) that is polynomial both in n and m and holds for an arbitrary infinite base field (regardless of the characteristic). A lower bound for d(n,2) due to Kuzmin is also extended to positive characteristic.
Recent results of Derksen and Makam on generators of rings of matrix invariants together with a theorem of Zubkov from 1996 yield an explicit upper bound on d(n,m) that is polynomial both in n and m and holds for an arbitrary infinite base field (regardless of the characteristic). A lower bound for d(n,2) due to Kuzmin is also extended to positive characteristic.
Everybody is invited.
Algebra and Logic Department, IMI – BAS