On Quasi-Harada Rings

Baba, Yoshitomo; Iwase, Ken-ichi

doi:10.1006/jabr.1996.0339

Cited by 13 publications

(6 citation statements)

References 14 publications

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“…Left and right quasi-Harada rings are called quasi-Harada rings. (See [8].) We can apply Lemma 2.3 to left quasi-Harada rings.…”

Section: Relations Between Quasi-harada Rings and Qf Ringsmentioning

confidence: 97%

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Self-duality of quasi-Harada rings and locally distributive rings

Koike

2006

Journal of Algebra

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Recently Y. Baba [Y. Baba, On self-duality of Auslander rings of local serial rings, Comm. Algebra 30 (6) (2002) 2583-2592] proved that certain quasi-Harada rings have a self-duality. In this paper, we also investigate left quasi-Harada rings and obtain several results including an improvement of the result of Y. Baba and applications to self-duality of locally distributive rings. Particularly we shall obtain several results related to Azumaya's conjecture ("every exact artinian ring has a self-duality"). 0. Introduction Y. Baba and K. Iwase [8] called a left artinian ring R a left quasi-Harada ring in case every finitely generated projective right R-module is quasi-injective. Symmetrically right quasi-Harada rings are defined. Left and right quasi-Harada rings are called quasi-Harada rings. Recently Y. Baba [7, Theorem 5] proved that if a quasi-Harada ring R satisfies the two conditions:( * ) gRg is a local serial ring; ( * * ) rad(gRg)\ rad(gRg) 2 contains a central element of gRg, then R has a self-duality, where g is an idempotent of R with gR a minimal faithful right Rmodule. In this paper, we notice that gRg ∼ = End R (gR) and End R (E(R R )) are Morita equivalent

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“…Left and right quasi-Harada rings are called quasi-Harada rings. (See [8].) We can apply Lemma 2.3 to left quasi-Harada rings.…”

Section: Relations Between Quasi-harada Rings and Qf Ringsmentioning

confidence: 97%

“…We now cite several basic properties of left quasi-Harada rings from [5,8]. Recall that a semiperfect ring R is a right QF-2 ring in case every indecomposable projective right R-module has simple essential socle.…”

Section: Proofmentioning

confidence: 99%

Self-duality of quasi-Harada rings and locally distributive rings

Koike

2006

Journal of Algebra

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“…. , : T ¬ R such that T is type * and Ker is a simple two-sided 3 n n 1 i Ž . ideal of T for i s 1, .…”

Section: ¢ §mentioning

confidence: 99%

Self-Duality and Harada Rings

Kado

Oshiro

1999

Journal of Algebra

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“…. , n(i)} (see, for instance, [3,Theorem B]). We call the {e i,j } m n(i) i=1,j=1 a left well indexed set of R. (Symmetrically, we also define a right well indexed set for a right Harada ring.…”

Section: Introductionmentioning

confidence: 99%