Tor algebra of local rings with decomposable maximal ideal

Saeed Nasseh; Maiko Ono; Yuji Yoshino

doi:10.1007/s00013-025-02200-3

Tor algebra of local rings with decomposable maximal ideal

Saeed Nasseh
, Maiko Ono
, Yuji Yoshino

Mathematical Sciences

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

Abstract

Let (R,mR) be a commutative noetherian local ring. Assuming that mR=I⊕J is a direct sum decomposition, where I and J are non-zero ideals of R, we describe the structure of the Tor algebra of R in terms of the Tor algebras of the rings R/I and R/J.

Original language	English
Journal	Archiv der Mathematik
DOIs	https://doi.org/10.1007/s00013-025-02200-3
State	Published - Nov 27 2025

Scopus Subject Areas

General Mathematics

Keywords

Avramov’s machine
Decomposable maximal ideal
DG algebra
Fiber product
Koszul complex
Tor algebra
Trivial extension

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10.1007/s00013-025-02200-3

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title = "Tor algebra of local rings with decomposable maximal ideal",

abstract = "Let (R,mR) be a commutative noetherian local ring. Assuming that mR=I⊕J is a direct sum decomposition, where I and J are non-zero ideals of R, we describe the structure of the Tor algebra of R in terms of the Tor algebras of the rings R/I and R/J.",

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author = "Saeed Nasseh and Maiko Ono and Yuji Yoshino",

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AU - Ono, Maiko

AU - Yoshino, Yuji

N1 - Publisher Copyright: © Springer Nature Switzerland AG 2025.

PY - 2025/11/27

Y1 - 2025/11/27

N2 - Let (R,mR) be a commutative noetherian local ring. Assuming that mR=I⊕J is a direct sum decomposition, where I and J are non-zero ideals of R, we describe the structure of the Tor algebra of R in terms of the Tor algebras of the rings R/I and R/J.

AB - Let (R,mR) be a commutative noetherian local ring. Assuming that mR=I⊕J is a direct sum decomposition, where I and J are non-zero ideals of R, we describe the structure of the Tor algebra of R in terms of the Tor algebras of the rings R/I and R/J.

KW - Avramov’s machine

KW - Decomposable maximal ideal

KW - DG algebra

KW - Fiber product

KW - Koszul complex

KW - Tor algebra

KW - Trivial extension

UR - https://www.scopus.com/pages/publications/105023147361

U2 - 10.1007/s00013-025-02200-3

DO - 10.1007/s00013-025-02200-3

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AN - SCOPUS:105023147361

SN - 0003-889X

JO - Archiv der Mathematik

JF - Archiv der Mathematik

ER -

Tor algebra of local rings with decomposable maximal ideal

Abstract

Scopus Subject Areas

Keywords

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