Examples of QF Rings without Nakayama Automorphism and H-Rings without Self-Duality

Koike, Kazutoshi

doi:10.1006/jabr.2001.8767

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2002

2008

Publication Types

Select...

Article3

Relationship

Self Cite1

Independent2

Authors

Journals

Cited by 3 publications

(1 citation statement)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…So we naturally have the question: Whether left Harada rings have self-dualities or not. This problem was first considered in [9] and solved negatively by K. Koike in [10]. So we have another question: What kind of left Harada rings have self-dualities.…”

Section: Introductionmentioning

confidence: 94%

Self-Duality of Harada Ring of a Component Type

Baba

2008

J. Algebra Appl.

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 94%

Self-Duality of Harada Ring of a Component Type

Baba

2008

J. Algebra Appl.

View full text Add to dashboard Cite

show abstract

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

Koike

2006

Journal of Algebra

Self Cite

View full text Add to dashboard Cite

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

show abstract

Almost self-duality and Harada rings

Koike

2002

Journal of Algebra

View full text Add to dashboard Cite

Examples of QF Rings without Nakayama Automorphism and H-Rings without Self-Duality

Cited by 3 publications

References 7 publications

Self-Duality of Harada Ring of a Component Type

Self-Duality of Harada Ring of a Component Type

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

Almost self-duality and Harada rings

Contact Info

Product

Resources

About