This article is cited in 2 papers

Ideals Generated by Reverse Lexicographic Segments

M. Crupi, M. La Barbiera

University of Messina

Abstract: Let $k$ be a field, and let $S=k[x_1,\dots,x_n]$ be the polynomial ring in $x_1,\dots,x_n$ with coefficients in the field $k$. We study ideals of $S$ which are generated by reverse lexicographic segments of monomials of $S$. An ideal generated by a reverse lexicographic segment is called a completely reverse lexicographic segment ideal if all iterated shadows of the set of generators are reverse lexicographic segments. We characterize all completely reverse lexicographic segment ideals of $S$ and determine conditions under which they have a linear resolution.

Keywords: polynomial ring, ideal, reverse lexicographic segment, iterated shadow, linear resolution.

UDC: 512

Received: 21.09.2009

DOI: 10.4213/mzm8920

 English version: Mathematical Notes, 2011, 89:1, 68–81

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