A Constructive Method for Standard Borel Fixed Submodules with Given Extremal Betti Numbers
Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, Viale Ferdinando Stagno d’Alcontres 31, 98166 Messina, Italy
Academic Editor: Yang-Hui He
Received: 29 May 2017 / Revised: 9 October 2017 / Accepted: 17 October 2017 / Published: 1 November 2017
be a polynomial ring in n
variables over a field K
of any characteristic. Given a strongly stable submodule M
of a finitely generated graded free S
, we propose a method for constructing a standard Borel-fixed submodule
so that the extremal Betti numbers of M
, values as well as positions, are preserved by passing from M
. As a result, we obtain a numerical characterization of all possible extremal Betti numbers of any standard Borel-fixed submodule of a finitely generated graded free S
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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MDPI and ACS Style
Crupi, M. A Constructive Method for Standard Borel Fixed Submodules with Given Extremal Betti Numbers. Mathematics 2017, 5, 56.
Crupi M. A Constructive Method for Standard Borel Fixed Submodules with Given Extremal Betti Numbers. Mathematics. 2017; 5(4):56.
Crupi, Marilena. 2017. "A Constructive Method for Standard Borel Fixed Submodules with Given Extremal Betti Numbers." Mathematics 5, no. 4: 56.
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