Search results for "Negative - answer"
showing 3 items of 3 documents
On the identities of the Grassmann algebras in characteristicp>0
2001
In this note we exhibit bases of the polynomial identities satisfied by the Grassmann algebras over a field of positive characteristic. This allows us to answer the following question of Kemer: Does the infinite dimensional Grassmann algebra with 1, over an infinite fieldK of characteristic 3, satisfy all identities of the algebraM 2(K) of all 2×2 matrices overK? We give a negative answer to this question. Further, we show that certain finite dimensional Grassmann algebras do give a positive answer to Kemer's question. All this allows us to obtain some information about the identities satisfied by the algebraM 2(K) over an infinite fieldK of positive odd characteristic, and to conjecture ba…
Sharpness of uniform continuity of quasiconformal mappings onto s-John domains
2017
We construct examples to show the sharpness of uniform continuity of quasiconformal mappings onto $s$-John domains. Our examples also give a negative answer to a prediction in [7].
On Daugavet indices of thickness
2020
Inspired by R. Whitley's thickness index the last named author recently introduced the Daugavet index of thickness of Banach spaces. We continue the investigation of the behavior of this index and also consider two new versions of the Daugavet index of thickness, which helps us solve an open problem which connect the Daugavet indices with the Daugavet equation. Moreover, we will improve the formerly known estimates of the behavior of Daugavet index on direct sums of Banach spaces by establishing sharp bounds. As a consequence of our results we prove that, for every $0<\delta<2$, there exists a Banach space where the infimum of the diameter of convex combinations of slices of the unit ball i…