Finitely generated flat modules and a characterization of semiperfect rings

Alberto Facchini; Dolors Herbera; Iskhak Sakhajev

doi:10.1081/AGB-120022787

Finitely generated flat modules and a characterization of semiperfect rings

Alberto Facchini, Dolors Herbera, Iskhak Sakhajev

Departament de Matemàtiques

Producció científica: Contribució a revista › Article › Recerca › Avaluat per experts

17 Cites (Scopus)

Resum

Per a un anell S, deixeu que K0(FGFl(S)) i K0(FGPr(S)) denotin els grups de Grothendieck de la categoria de tots els mòduls plans finitament generats i la categoria de tots els mòduls projectius 5-finits respectivament. Demostrem que un anell semilocal R és semiperfecte si i només si el grup homomorfisme K0(FGFl(R)) → K0(FGFl(R/J(R))) és un epimorfisme i K0(FGFl(R)) = K0(FGPr(R)).

Idioma original	Anglès
Pàgines (de-a)	4195-4214
Revista	Communications in Algebra
Volum	31
DOIs	https://doi.org/10.1081/AGB-120022787
Estat de la publicació	Publicada - 1 de set. 2003

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10.1081/AGB-120022787

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@article{f16432f1bf90447592cbc52e7dda071e,

title = "Finitely generated flat modules and a characterization of semiperfect rings",

abstract = "For a ring S, let K0(FGFl(S)) and K0(FGPr(S)) denote the Grothendieck groups of the category of all finitely generated flat 5-modules and the category of all finitely generated projective 5-modules respectively. We prove that a semilocal ring R is semiperfect if and only if the group homomorphism K0(FGFl(R)) → K0(FGFl(R/J(R))) is an epimorphism and K0(FGFl(R)) = K0(FGPr(R)).",

keywords = "Flat modules, Lifting idempotents, Semilocal rings, Semiperfect rings",

author = "Alberto Facchini and Dolors Herbera and Iskhak Sakhajev",

year = "2003",

month = sep,

day = "1",

doi = "10.1081/AGB-120022787",

language = "English",

volume = "31",

pages = "4195--4214",

journal = "Communications in Algebra",

issn = "0092-7872",

publisher = "Taylor and Francis Ltd.",

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TY - JOUR

T1 - Finitely generated flat modules and a characterization of semiperfect rings

AU - Facchini, Alberto

AU - Herbera, Dolors

AU - Sakhajev, Iskhak

PY - 2003/9/1

Y1 - 2003/9/1

N2 - For a ring S, let K0(FGFl(S)) and K0(FGPr(S)) denote the Grothendieck groups of the category of all finitely generated flat 5-modules and the category of all finitely generated projective 5-modules respectively. We prove that a semilocal ring R is semiperfect if and only if the group homomorphism K0(FGFl(R)) → K0(FGFl(R/J(R))) is an epimorphism and K0(FGFl(R)) = K0(FGPr(R)).

AB - For a ring S, let K0(FGFl(S)) and K0(FGPr(S)) denote the Grothendieck groups of the category of all finitely generated flat 5-modules and the category of all finitely generated projective 5-modules respectively. We prove that a semilocal ring R is semiperfect if and only if the group homomorphism K0(FGFl(R)) → K0(FGFl(R/J(R))) is an epimorphism and K0(FGFl(R)) = K0(FGPr(R)).

KW - Flat modules

KW - Lifting idempotents

KW - Semilocal rings

KW - Semiperfect rings

UR - https://www.scopus.com/pages/publications/0042384446

U2 - 10.1081/AGB-120022787

DO - 10.1081/AGB-120022787

M3 - Article

SN - 0092-7872

VL - 31

SP - 4195

EP - 4214

JO - Communications in Algebra

JF - Communications in Algebra

ER -

Finitely generated flat modules and a characterization of semiperfect rings

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