On split-by-nilpotent extensions

Ibrahim Assem; Dan Zacharia

doi:10.4064/cm98-2-10

On split-by-nilpotent extensions

Ibrahim Assem, Dan Zacharia

Department of Mathematics

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

18 Scopus citations

Abstract

Let A and R be two artin algebras such that R is a split extension of A by a nilpotent ideal. We prove that if R is quasi-tilted, or tame and tilted, then so is A. Moreover, generalizations of these properties, such as laura and shod, are also inherited. We also study the relationship between the tilting R-modules and the tilting A-modules.

Original language	English (US)
Pages (from-to)	259-275
Number of pages	17
Journal	Colloquium Mathematicum
Volume	98
Issue number	2
DOIs	https://doi.org/10.4064/cm98-2-10
State	Published - 2003

Keywords

Quasi-tilted algebras
Split algebras
Tilted algebras
Tilting modules

ASJC Scopus subject areas

General Mathematics

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10.4064/cm98-2-10

Cite this

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AU - Zacharia, Dan

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AB - Let A and R be two artin algebras such that R is a split extension of A by a nilpotent ideal. We prove that if R is quasi-tilted, or tame and tilted, then so is A. Moreover, generalizations of these properties, such as laura and shod, are also inherited. We also study the relationship between the tilting R-modules and the tilting A-modules.

KW - Quasi-tilted algebras

KW - Split algebras

KW - Tilted algebras

KW - Tilting modules

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JO - Colloquium Mathematicum

JF - Colloquium Mathematicum

IS - 2

ER -

On split-by-nilpotent extensions

Abstract

Keywords

ASJC Scopus subject areas

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