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Practical algebraic calculus and Nullstellensatz with the checkers Pacheck and Pastèque and Nuss-Checker. [PDF]
Form Methods Syst DesKaufmann D, Fleury M, Biere A, Kauers M.
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Identifiability of Phylogenetic Level-2 Networks under the Jukes-Cantor Model
Englander AK +6 more
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k-Decomposable Monomial Ideals
Algebra Colloquium, 2015In this paper we introduce a class of monomial ideals, called k-decomposable ideals. It is shown that the class of k-decomposable ideals is contained in the class of monomial ideals with linear quotients, and when k is large enough, the class of k-decomposable ideals is equal to the class of ideals with linear quotients. In addition, it is shown that a
Rahmati-Asghar, Rahim, Yassemi, Siamak
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Superficial ideals for monomial ideals
Journal of Algebra and Its Applications, 2018Let [Formula: see text] and [Formula: see text] be two ideals in a commutative Noetherian ring [Formula: see text]. We say that [Formula: see text] is a superficial ideal for [Formula: see text] if the following conditions are satisfied: (i) [Formula: see text], where [Formula: see text] denotes a minimal set of generators of an ideal [Formula: see ...
Rajaee, Saeed +2 more
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Journal of Mathematical Sciences, 2007
The author studies the numerical characteristics of monomial ideals in polynomial rings \(A=k[x_1,\ldots x_n]\) and in exterior algebras \(E\) on the same number of variables. In Chapter 2 of the paper, the author generalizes Macaulay's theorem to quotient rings. That is, the author gives conditions on and ideal \(I\) and on ideals \(J\) containing \(I\
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The author studies the numerical characteristics of monomial ideals in polynomial rings \(A=k[x_1,\ldots x_n]\) and in exterior algebras \(E\) on the same number of variables. In Chapter 2 of the paper, the author generalizes Macaulay's theorem to quotient rings. That is, the author gives conditions on and ideal \(I\) and on ideals \(J\) containing \(I\
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Monomial ideals with tiny squares and Freiman ideals
Czechoslovak Mathematical Journal, 2021Throughout this paper, let \(K\) be a field and \(R=K[x,y]\) a polynomial ring over \(K\) with two variables. For a monomial ideal \(I\) of \(R\), let \(\mu(I)\) be the number of the least monomial generators. In the paper, the authors provide a construction of monomial ideals \(I\) such that \(\mu(I^2)
Al-Ayyoub, Ibrahim, Nasernejad, Mehrdad
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Manuscripta Mathematica, 1979
The paper concerns itself with generating sets for monomial Gorenstein ideals in polynomial rings k[x1,..., xr], k an arbitrary field. For r=5 it is shown that for a certain class of these ideals, the number of generators is bounded by 13. To establish the sharpness of this bound an algorithm is established, to obtain all numerical symmetric semigroups
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The paper concerns itself with generating sets for monomial Gorenstein ideals in polynomial rings k[x1,..., xr], k an arbitrary field. For r=5 it is shown that for a certain class of these ideals, the number of generators is bounded by 13. To establish the sharpness of this bound an algorithm is established, to obtain all numerical symmetric semigroups
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Associated radical ideals of monomial ideals
Communications in Algebra, 2018AbstractAlgebraic and combinatorial properties of a monomial ideal are studied in terms of its associated radical ideals. In particular, we present some applications to the symbolic powers of square-free monomial ideals.
Raheleh Jafari, Hossein Sabzrou
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2018
In this chapter, we apply some of the operations of Appendix A to monomial ideals. We have already seen this theme for sums and products in Exercises 1.3.12 and 1.3.13. In Section 2.1 we show, for instance, that intersections of monomial ideals are monomial ideals.
W. Frank Moore +2 more
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In this chapter, we apply some of the operations of Appendix A to monomial ideals. We have already seen this theme for sums and products in Exercises 1.3.12 and 1.3.13. In Section 2.1 we show, for instance, that intersections of monomial ideals are monomial ideals.
W. Frank Moore +2 more
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