Remarks on Balance in Generalized Tate Cohomology

Alina Iacob

doi:10.1007/s00013-005-1399-6

Remarks on Balance in Generalized Tate Cohomology

Alina Iacob

Mathematical Sciences

University of Kentucky

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

<div class="line" id="line-19"> We consider two pairs of complete hereditary cotorsion theories ( P , M ),( M , I )and( C , L )( L , E ) on the category of left R -modules, such that P ⊂ C . We prove that for any left R -modules M ,  N and for any n  &geqq; 1, the generalized Tate cohomology modules Ext &circ; n C , P ( M , N ) can be computed either using a left C  - resolution of M and a left P  - resolution of M or using a right E -and a right I  - resolution of N .</div>

Original language	American English
Journal	Archiv der Mathematik
Volume	85
DOIs	https://doi.org/10.1007/s00013-005-1399-6
State	Published - Oct 2005

Disciplines

Physical Sciences and Mathematics

Keywords

Balance
Generalized Tate cohomology

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title = "Remarks on Balance in Generalized Tate Cohomology",

abstract = " We consider two pairs of complete hereditary cotorsion theories ( P , M ),( M , I )and( C , L )( L , E ) on the category of left R -modules, such that P ⊂ C . We prove that for any left R -modules M ,  N and for any n  &geqq; 1, the generalized Tate cohomology modules Ext &circ; n C , P ( M , N ) can be computed either using a left C  - resolution of M and a left P  - resolution of M or using a right E -and a right I  - resolution of N .",

keywords = "Balance, Generalized Tate cohomology",

author = "Alina Iacob",

note = "We co nsider two pairs of complete hereditary cotorsio n theories $${\left( {\mathcal{P},\mathcal{ M}} \right)},{\left( {\mathcal{ M},\mathcal{I}} \right)}\;{\text{a nd}}\;{\left( {\mathcal{C},\mathca",

year = "2005",

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doi = "10.1007/s00013-005-1399-6",

language = "American English",

volume = "85",

journal = "Archiv der Mathematik",

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publisher = "Birkhauser Verlag Basel",

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AU - Iacob, Alina

N1 - We co nsider two pairs of complete hereditary cotorsio n theories $${\left( {\mathcal{P},\mathcal{ M}} \right)},{\left( {\mathcal{ M},\mathcal{I}} \right)}\;{\text{a nd}}\;{\left( {\mathcal{C},\mathca

PY - 2005/10

Y1 - 2005/10

N2 - We consider two pairs of complete hereditary cotorsion theories ( P , M ),( M , I )and( C , L )( L , E ) on the category of left R -modules, such that P ⊂ C . We prove that for any left R -modules M ,  N and for any n  &geqq; 1, the generalized Tate cohomology modules Ext &circ; n C , P ( M , N ) can be computed either using a left C  - resolution of M and a left P  - resolution of M or using a right E -and a right I  - resolution of N .

AB - We consider two pairs of complete hereditary cotorsion theories ( P , M ),( M , I )and( C , L )( L , E ) on the category of left R -modules, such that P ⊂ C . We prove that for any left R -modules M ,  N and for any n  &geqq; 1, the generalized Tate cohomology modules Ext &circ; n C , P ( M , N ) can be computed either using a left C  - resolution of M and a left P  - resolution of M or using a right E -and a right I  - resolution of N .

KW - Balance

KW - Generalized Tate cohomology

UR - https://doi.org/10.1007/s00013-005-1399-6

U2 - 10.1007/s00013-005-1399-6

DO - 10.1007/s00013-005-1399-6

M3 - Article

SN - 0003-889X

VL - 85

JO - Archiv der Mathematik

JF - Archiv der Mathematik

ER -

Remarks on Balance in Generalized Tate Cohomology

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