Last edited by Milmaran
Monday, August 10, 2020 | History

2 edition of Lectures on QF-3 and QF-1 rings found in the catalog.

Lectures on QF-3 and QF-1 rings

Hiroyuki Tachikawa

Lectures on QF-3 and QF-1 rings

by Hiroyuki Tachikawa

  • 13 Want to read
  • 3 Currently reading

Published by Dept. of Mathematics, Carleton University] in [Ottawa .
Written in English

    Subjects:
  • Quasi-Frobenius rings.

  • Edition Notes

    Bibliography: leaves [118]-[120]

    Statementby Hiroyuki Tachikawa ; notes by Claus Michael Ringel.
    SeriesCarleton mathematical lecture notes -- no.1, Carleton mathematical lecture notes -- no. 1
    The Physical Object
    Paginationv, 117,[3] leaves ;
    Number of Pages117
    ID Numbers
    Open LibraryOL22056833M

    準フロベニウス環の他の種々の一般化には QF-1, QF-2, QF-3 環がある。 Lectures on modules and rings, Graduate Texts in Mathematics No. , Berlin, New York: Springer-Verlag, References. For QF-1, QF-2, QF-3 rings: Morita, Kiiti (), “On algebras for which every faithful representation is .   COVID campus closures: see options for getting or retaining Remote Access to subscribed content.

    B. Müller [Mu68b] proved a structure theorem for QF-3 algebras: An algebra A is a QF-3 algebra if and only if A is a subalgebra of a QF-3 maximal quotient algebra R such that A contains suitable minimal faithful ideals R Re, fR R and the unit 1 of R. See [RinT75] for a generalization to arbitrary QF-3 rings. Baba [On Harada rings and quasi-Harada rings with left global dimension at most 2. Comm. Algebra28(6) () ] proved that every left Harada rings with .

    Quasi-Frobenius Rings and Generalizations QF-3 and QF-1 Rings (Lecture Notes in Mathematics) (Volume 0) by Hiroyuki Tachikawa, Claus Michael Ringel Paperback, Pages, Published by Springer ISBN , ISBN: Other diverse generalizations of quasi-Frobenius rings include QF-1, QF-2 and QF-3 rings. These types of rings can be viewed as descendants of algebras examined by Georg Frobenius. A partial list of pioneers in quasi-Frobenius rings includes R. Brauer, K. Morita, .


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Lectures on QF-3 and QF-1 rings by Hiroyuki Tachikawa Download PDF EPUB FB2

Quasi-Frobenius Rings and Generalizations: QF-3 and QF-1 Rings (Lecture Notes in Mathematics) rd Edition by Hiroyuki Tachikawa (Author) › Visit Amazon's Hiroyuki Tachikawa Page. Find all the books, read about the author, and more. See search results for this author. Are you an author.

Cited by: Additional Physical Format: Online version: Tachikawa, Hiroyuki, Lectures on QF-3 and QF-1 rings. [Ottawa: Carleton University], (OCoLC) Quasi-Frobenius Rings and Generalizations QF-3 and QF-1 Rings Notes by Claus Michael Ringel.

Authors; 61 Citations; k Downloads; Part of the Lecture Notes in Mathematics book series (LNM, volume ) Log in to check access. Buy eBook.

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Cite this chapter as: Tachikawa H. () Left QF-3 rings. In: Quasi-Frobenius Rings and Generalizations QF-3 and QF-1 Rings. Lecture Notes in Mathematics, vol Author: Hiroyuki Tachikawa. Cite this chapter as: Tachikawa H.

() The structure of QF-3 rings. In: Quasi-Frobenius Rings and Generalizations QF-3 and QF-1 Rings. Lecture Notes in Mathematics, vol Tachikawa H. () QF-3 rings and categories of projective modules. In: Quasi-Frobenius Rings and Generalizations QF-3 and QF-1 Rings.

Lecture Notes in Mathematics, vol   Cite this chapter as: Tachikawa H. () QF rings. In: Quasi-Frobenius Rings and Generalizations QF-3 and QF-1 Rings. Lecture Notes in Mathematics, vol QF-3 rings results known to hold for QF-3 algebras almost from their inception. Specifically, Jans [7] has characterized QF-3 rings as those artinian rings whose left injective hulls are projective and Harada [5] has shown that the QF-3 property is actually "two-sided" (i.e., a QF-3 ring.

1, 3, 9 is based on experience. According to Lou Cohen in his book “Quality Function Deployment – How to make QFD work for you” early practitioners in the US used 1, 3, 5 but needed a stronger contrast between “strong” and the other impacts. “9” was adopted for that purpose on the basis that it had been seen to be used in Japan in the early 80’s.

ALMOST QF RINGS most QF. The following is dual to Corollary to Theorem 1. Proposition 1. Let R be an artinian ring. Then R is right almost QF1 if and only if I): R is right QF-2*, 2): R is right QF-3* and 3): if eR/A is injectίve for-4ΦO, then eR/B is uniform for any BdA.

1) together with 2) is equivalent to 4): every indecomposable infective is a factor module of some local protective. Quasi-Frobenius Rings and Generalizations: QF-3 and QF-1 Rings (Lecture Notes in Mathematics) (Volume 0) by Hiroyuki Tachikawa, Claus Michael Ringel Paperback, Pages, Published ISBN / ISBN / Harada extended these results to left QF-3 and semi-primary partially PP-rings by using his own terminology.

In Colby and Rutter applied their theory to extend some of the results for. Right K-QF 3 rings share with right QF 3 rings several known proper- ties and Kawada gave in his paper a way to build examples of such rings (see [10, Theorem ]). The purpose of the present paper is the study of right S-QF 3 rings with zero singular right ideal.

Carl Faith in introduced and investigated an interesting class of rings over which every cyclic right module has Σ-injective injective hull (abbr., right CSI-rings) [ Faith, C.

[6] H. Tachikawa, Lectures on QF and QF Rings, Carleton Mathematical Lecture Notes No. 1, July, Mathematical Reviews (MathSciNet): MR Zentralblatt MATH: Pacific Journal of Mathematics, A Non-profit Corporation.

Preliminaries --Semi-perfect rings --Morita duality --Left QF-3 rings --The structure of QF-3 rings --Are noetherian, left QF-3 rings artinian, so QF-3. -- Dominant dimension -- Conjectures arising from Nakayama's conjecture -- QF-3 rings and rings of finite representation type -- The double centralizer condition -- QF rings -- QF-3 rings.

The structure of QF-3 rings.- Are noetherian, left QF-3 rings artinian, so QF-3?.- Dominant dimension.- Conjectures arising from Nakayama's conjecture.- QF-3 rings and rings of finite representation type.- The double centralizer condition.- QF rings.- QF-3 rings and categories of projective modules.

Series Title: Lecture notes in mathematics. Get this from a library. Quasi-Frobenius rings and generalizations ; QF-3 and QF-1 rings.

[Hiroyuki Tachikawa]. Semi-perfect rings.- Morita duality.- Left QF-3 rings.- The structure of QF-3 rings.- Are noetherian, left QF-3 rings artinian, so QF-3?.- Dominant dimension.- Conjectures arising from Nakayama's conjecture.- QF-3 rings and rings of finite representation type.- The double centralizer condition.- QF rings.- QF-3 rings and categories of.

JOL'RNAI. OF ALGE () QF-3 Rings and Categories of Projective Modules HIROYDKI TACHIKAWA Tokyo University of Education, Otsiika, Bunkyo-ku, Tokyo, Japan Communicated by P. M. Co/in Received Septem In [2] M. Auslander proved that for Artin algebras there is a one-to-one correspondence between Morita equivalence classes of QF-3 maximal quotient rings.

C. M. RINGEL, Socle conditions for QF-1 rings, Pacific J. Math. 41 (), 7. H. TACHIKAWA, On rings for which every indecomposable right module has a unique maximal submodule, Math. Z. 71 (), 8- H. TACHIKAWA, On algebras of which every indecomposable representation has an irreducible one as the top or the bottom Loewy.The QF 3 inch 20 cwt anti-aircraft gun became the standard anti-aircraft gun used in the home defence of the United Kingdom against German airships and bombers and on the Western Front in World War was also common on British warships in World War I and submarines in World War II.

20 cwt referred to the weight of the barrel and breech, to differentiate it from other "3 inch" guns (1 cwt.