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- 16-XX Associative rings and algebras
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Assume that k is a field of characteristic different from 2. We show that if Γ is a strongly simply connected k-algebra of non-polynomial growth, then there exists a special family of pointed Γ-modules, called an independent pair of dense chains of pointed modules. Then it follows by a result of Ziegler that Γ admits a super-decomposable pure-injective module if k is a countable field.
Let A be a finite-dimensional algebra over an algebraically closed field with radical square zero, and such that all simple A-modules have dimension at most two. We give a characterization of those A that have finitely many conjugacy classes of left ideals.
Let G be a finite p-group and let F be the field of p elements. It is shown that if G is elementary abelian-by-cyclic then the isomorphism type of G is determined by FG.
In this paper, we study the situation as to when the unit group U(KG) of a group algebra KG equals K*G(1 + J(KG)), where K is a field of characteristic p > 0 and G is a finite group.
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