On two conjectures of Faith

JOURNAL OF ALGEBRA

卷:367

Article

Haim, M.²  Iovanov, M. C.^3,4  Torrecillas, B.¹ 

[1] Univ Almeria, Dept Algebra & Anal Matemat, Almeria 04071, Spain

[2] Univ Republica, Fac Ciencias, Montevideo 11400, Uruguay

[3] Univ Bucharest, Fac Matemat & Informat, Bucharest 010014, Romania

[4] Univ So Calif, Los Angeles, CA 90089 USA

关键词: QF ring;    PF ring;    Ultrafilter;    Coalgebra;    FGF conjecture;    Faith conjecture;   

DOI  :  10.1016/j.jalgebra.2012.06.003

来源: Elsevier

【 摘 要 】

We prove that a profinite algebra whose left (right) cyclic modules are torsionless is finite dimensional and QF. We give a relative version of the notion of left (right) PF ring for pseudocompact algebras and prove it is left-right symmetric and dual to the notion of quasi-co-Frobenius coalgebras. We also prove two ring theoretic conjectures of Faith, in the setting (and supplementary hypothesis) of profinite algebras: any profinite semiartinian selfinjective algebra is finite dimensional and QF, and any FGF profinite algebra is finite dimensional QF. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free