The central nilradical of nonnoetherian dimer algebras
Beil, Charlie
arXiv, Tome 2019 (2019) no. 0, / Harvested from
Let $Z$ be the center of a nonnoetherian dimer algebra on a torus. We show that the nilradical $\operatorname{nil}Z$ of $Z$ is prime, may be nonzero, and consists precisely of the central elements that vanish under a cyclic contraction. This implies that the nonnoetherian scheme $\operatorname{Spec}Z$ is irreducible. We also show that the reduced center $\hat{Z} = Z/\operatorname{nil}Z$ embeds into the center $R$ of the corresponding homotopy algebra, and that their normalizations are equal. Finally, we characterize the normality of $R$, and show that if $\hat{Z}$ is normal, then it has the special form $k + J$ where $J$ is an ideal of the cycle algebra.
Publié le : 2019-02-28
Classification:  Mathematics - Rings and Algebras 
@article{1902.11299,
     author = {Beil, Charlie},
     title = {The central nilradical of nonnoetherian dimer algebras},
     journal = {arXiv},
     volume = {2019},
     number = {0},
     year = {2019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1902.11299}
}

Beil, Charlie. The central nilradical of nonnoetherian dimer algebras. arXiv, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/1902.11299/