Mathematics - Research News

Finite unions of overrings of an integral domain

 Mathematics - Research News
 13 May 2020
Christian Gottlieb. Source: Journal of Commutative Algebra, Volume 12, Number 1, 87--90.Abstract: Let [math] be an integral domain, and let [math] be overrings of [math] , where [math] is of the form [math] , where [math] for some prime ideals [math] , and where each [math] , [math] , is of the...

A Gröbner basis for the graph of the reciprocal plane

 Mathematics - Research News
 13 May 2020
Alex Fink, David E. Speyer, Alexander Woo. Source: Journal of Commutative Algebra, Volume 12, Number 1, 77--86.Abstract: Given the complement of a hyperplane arrangement, let [math] be the closure of the graph of the map inverting each of its defining linear forms. The characteristic polynomial...

Computing general strongly stable modules with given extremal Betti numbers

 Mathematics - Research News
 13 May 2020
Marilena Crupi. Source: Journal of Commutative Algebra, Volume 12, Number 1, 53--70.Abstract: Let [math] be a polynomial ring in [math] variables over a field [math] of any characteristic. Let [math] be a strongly stable submodule of a finitely generated graded free [math] -module [math] , with...

Kronecker function rings and power series rings

 Mathematics - Research News
 13 May 2020
Gyu Whan Chang. Source: Journal of Commutative Algebra, Volume 12, Number 1, 27--51.Abstract: Let [math] be an integral domain with quotient field [math] , [math] be an indeterminate over [math] , [math] be the power series ring over [math] , and [math] be the ideal of [math] generated by the...

On the Gorenstein defect categories

 Mathematics - Research News
 13 May 2020
Javad Asadollahi, Tahereh Dehghanpour, Rasool Hafezi. Source: Journal of Commutative Algebra, Volume 12, Number 1, 1--26.Abstract: The main theme of this paper is to study different “Gorenstein defect categories” and their connections. This is done by studying rings for which [math] , that is,...

The $p$-radical closure of local noetherian rings

 Mathematics - Research News
 13 May 2020
Stefan Schröer. Source: Journal of Commutative Algebra, Volume 12, Number 1, 135--151.Abstract: Given a local noetherian ring [math] whose formal completion is integral, we introduce and study the [math] -radical closure [math] . Roughly speaking, this is the largest purely inseparable [math]...

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