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LINEAR QUOTIENTS AND MULTIGRADED SHIFTS OF BOREL IDEALS

Part of: Algebraic combinatorics General commutative ring theory Commutative algebra: Homological methods Arithmetic rings and other special rings

Published online by Cambridge University Press:  30 January 2019

SHAMILA BAYATI Open the ORCID record for SHAMILA BAYATI [Opens in a new window] ,
IMAN JAHANI Open the ORCID record for IMAN JAHANI [Opens in a new window]  and
NADIYA TAGHIPOUR Open the ORCID record for NADIYA TAGHIPOUR [Opens in a new window]
SHAMILA BAYATI*
Affiliation:
Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Ave., Tehran 15914, Iran email [email protected]
IMAN JAHANI
Affiliation:
Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Ave., Tehran 15914, Iran email [email protected]
NADIYA TAGHIPOUR
Affiliation:
Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Ave., Tehran 15914, Iran email [email protected]
*
✉[email protected]
Rights & Permissions [Opens in a new window]

Abstract

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We investigate whether the property of having linear quotients is inherited by ideals generated by multigraded shifts of a Borel ideal and a squarefree Borel ideal. We show that the ideal generated by the first multigraded shifts of a Borel ideal has linear quotients, as do the ideal generated by the $k$th multigraded shifts of a principal Borel ideal and an equigenerated squarefree Borel ideal for each $k$. Furthermore, we show that equigenerated squarefree Borel ideals share the property of being squarefree Borel with the ideals generated by multigraded shifts.

Keywords

Borel idealfree resolutionlinear quotientmultigraded shiftsquarefree Borel ideal

MSC classification

Primary: 13D02: Syzygies, resolutions, complexes
Secondary: 13A02: Graded rings 13F20: Polynomial rings and ideals; rings of integer-valued polynomials 05E40: Combinatorial aspects of commutative algebra
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 100 , Issue 1 , August 2019 , pp. 48 - 57
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

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