Noncoherent initial ideals in exterior algebras
Dominic Searles, Arkadii Slinko
TL;DR
This paper constructs a noncoherent initial ideal in the exterior algebra of order 6, providing a method to generate such ideals using specific noncoherent term orders, thus addressing a question from 2000.
Contribution
It introduces a novel construction of noncoherent initial ideals in exterior algebras and a method to generate them using noncoherent term orders.
Findings
Constructed a noncoherent initial ideal in exterior algebra of order 6
Provided a general method for constructing noncoherent initial ideals
Answered a longstanding question by D. Maclagan (2000)
Abstract
We construct a noncoherent initial ideal of an ideal in the exterior algebra of order 6, answering a question of D. Maclagan (2000). We also give a method for constructing noncoherent initial ideals in exterior algebras using certain noncoherent term orders.
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Taxonomy
TopicsRings, Modules, and Algebras · Commutative Algebra and Its Applications · Algebraic structures and combinatorial models