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Rafael H. Villarreal. Download (pdf, . 8 Mb) Donate Read. Epub FB2 mobi txt RTF. Converted file can differ from the original. If possible, download the file in its original format.
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by Mary Jane Sterling. monomial: An expression with only one term. polynomial: An expression with several terms. quadratic: An expression in which the highest power of any variable. ✓monomial: An expression with only one term. ✓polynomial: An expression with several terms. ✓quadratic: An expression in which the highest power of any variable.
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Proposition 2. Suppose f (x1,. xt, y) is a Lie polynomial in which y appears in degree 1 in each of its Lie monomials. Then f corresponds to an ad-polynomial taking on the same values on L as f. Proof. In view of Remark 1, it suces to show that any Lie monomial h can be rewritten in the free Lie algebra as a sum of Lie monomials in which y appears (in degree 1) in the innermost set of Lie brackets. This could be done directly by means of the Jacobi identity, but here is a slicker argument
We discuss several existent software packages and introduce our own contribution, a Monte Carlo based approach to the computation of volumes. Finally, we make comparisons of multiplicities of general ideals and of their initial ideals.
Normality of Rees Algebras of Monomial Ideals Integral closure of monomial ideals Normality criteria Rees cones and polymatroidal ideals Veronese subrings and the a-invariant Normalizations of Rees algebras Rees algebras of Veronese ideals Divisor class group of a Rees algebra Stochastic matrices and Cremona maps.
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Title: Monomial Algebras
Series: Monographs and Research Notes in Mathematics (Book 8)
Author: Rafael Villarreal
Hardcover: 704 pages
Publisher: Chapman and Hall/CRC; 2 edition (March 26, 2015)
Monomial Algebras, Second Edition presents algebraic, combinatorial, and computational methods for studying monomial algebras and their ideals, including Stanley–Reisner rings, monomial subrings, Ehrhart rings, and blowup algebras. It emphasizes square-free monomials and the corresponding graphs, clutters, or hypergraphs.
New to the Second Edition
- Four new chapters that focus on the algebraic properties of blowup algebras in combinatorial optimization problems of clutters and hypergraphs
- Two new chapters that explore the algebraic and combinatorial properties of the edge ideal of clutters and hypergraphs
- Full revisions of existing chapters to provide an up-to-date account of the subject
Bringing together several areas of pure and applied mathematics, this book shows how monomial algebras are related to polyhedral geometry, combinatorial optimization, and combinatorics of hypergraphs. It directly links the algebraic properties of monomial algebras to combinatorial structures (such as simplicial complexes, posets, digraphs, graphs, and clutters) and linear optimization problems.