Absolute, Gorenstein, and Tate Torsion Modules

Alina Iacob

doi:10.1080/00927870601169275

Absolute, Gorenstein, and Tate Torsion Modules

Alina Iacob

Mathematical Sciences

University of North Carolina at Wilmington

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

23 Scopus citations

Abstract

<div class="line" id="line-19"> We show that there is an Avramov–Martsinkovsky type exact sequence with <img src="http://www.tandfonline.com/na101/home/literatum/publisher/tandf/journals/content/lagb20/2007/lagb20.v035.i05/00927870601169275/production/images/lagb_a_216852_o_ilm0001.gif"/> , Gtor, and Tor. We prove that if R is a Gorenstein ring, then the modules <img src="http://www.tandfonline.com/na101/home/literatum/publisher/tandf/journals/content/lagb20/2007/lagb20.v035.i05/00927870601169275/production/images/lagb_a_216852_o_ilm0002.gif"/> , n ≥ 1 can be computed using either a complete resolution of MR or using a complete resolution of RN. We show that over a Gorenstein ring a left R-module N is Gorenstein flat if and only if <img src="http://www.tandfonline.com/na101/home/literatum/publisher/tandf/journals/content/lagb20/2007/lagb20.v035.i05/00927870601169275/production/images/lagb_a_216852_o_ilm0003.gif"/> . We also show that over commutative Gorenstein rings the modules <img src="http://www.tandfonline.com/na101/home/literatum/publisher/tandf/journals/content/lagb20/2007/lagb20.v035.i05/00927870601169275/production/images/lagb_a_216852_o_ilm0004.gif"/> can be computed by the combined use of a flat resolution and a Gorenstein flat resolution of M.</div>

Original language	American English
Journal	Communications in Algebra
Volume	35
DOIs	https://doi.org/10.1080/00927870601169275
State	Published - May 7 2007

Keywords

Complete resolution
Gorenstein flat resolution
Gorenstein projective resolution

DC Disciplines

Mathematics

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10.1080/00927870601169275License: Unspecified

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title = "Absolute, Gorenstein, and Tate Torsion Modules",

abstract = " We show that there is an Avramov–Martsinkovsky type exact sequence with , Gtor, and Tor. We prove that if R is a Gorenstein ring, then the modules , n ≥ 1 can be computed using either a complete resolution of MR or using a complete resolution of RN. We show that over a Gorenstein ring a left R-module N is Gorenstein flat if and only if . We also show that over commutative Gorenstein rings the modules can be computed by the combined use of a flat resolution and a Gorenstein flat resolution of M.",

keywords = "Complete resolution, Gorenstein flat resolution, Gorenstein projective resolution",

author = "Alina Iacob",

note = "(2007). Absolute, Gorenstein, and Tate Torsion Modules. Communications in Algebra: Vol. 35, No. 5, pp. 1589-1606.",

year = "2007",

month = may,

day = "7",

doi = "10.1080/00927870601169275",

language = "American English",

volume = "35",

journal = "Communications in Algebra",

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T1 - Absolute, Gorenstein, and Tate Torsion Modules

AU - Iacob, Alina

N1 - (2007). Absolute, Gorenstein, and Tate Torsion Modules. Communications in Algebra: Vol. 35, No. 5, pp. 1589-1606.

PY - 2007/5/7

Y1 - 2007/5/7

N2 - We show that there is an Avramov–Martsinkovsky type exact sequence with , Gtor, and Tor. We prove that if R is a Gorenstein ring, then the modules , n ≥ 1 can be computed using either a complete resolution of MR or using a complete resolution of RN. We show that over a Gorenstein ring a left R-module N is Gorenstein flat if and only if . We also show that over commutative Gorenstein rings the modules can be computed by the combined use of a flat resolution and a Gorenstein flat resolution of M.

AB - We show that there is an Avramov–Martsinkovsky type exact sequence with , Gtor, and Tor. We prove that if R is a Gorenstein ring, then the modules , n ≥ 1 can be computed using either a complete resolution of MR or using a complete resolution of RN. We show that over a Gorenstein ring a left R-module N is Gorenstein flat if and only if . We also show that over commutative Gorenstein rings the modules can be computed by the combined use of a flat resolution and a Gorenstein flat resolution of M.

KW - Complete resolution

KW - Gorenstein flat resolution

KW - Gorenstein projective resolution

UR - https://doi.org/10.1080/00927870601169275

U2 - 10.1080/00927870601169275

DO - 10.1080/00927870601169275

M3 - Article

SN - 0092-7872

VL - 35

JO - Communications in Algebra

JF - Communications in Algebra

ER -

Absolute, Gorenstein, and Tate Torsion Modules

Abstract

Keywords

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