3 citations · 3 across the 3 of their papers we have counts for
3 papers
math.RA2016★ 3 cited
Non-noetherian groups and primitivity of their group algebras
James Alexander, Tsunekazu Nishinaka
We prove that the group algebra of a group over a field is primitive, provided that has a free subgroup with the same cardinality as , and that satisfies th…
math.GR2016
Uncountable locally free groups and their group rings
Tsunekazu Nishinaka
In this note, we show that an uncountable locally free group, and therefore every locally free group, has a free subgroup whose cardinality is the same as that of . This result…
math.RA2010
Group rings of countable non-abelian locally free groups are primitive
Tsunekazu Nishinaka
We prove that every group ring of a non-abelian locally free group which is the union of an ascending sequence of free groups is primitive. In particular, every group ring of a cou…