Results 11 to 20 of about 14,720 (185)
Normality of Monomial Ideals [PDF]
Rocky Mountain Journal of Mathematics, 2010 Given the monomial ideal I=(x_1^{{\alpha}_1},...,x_{n}^{{\alpha}_{n}})\subset K[x_1,...,x_{n}] where {\alpha}_{i} are positive integers and K a field and let J be the integral closure of I .
Al-Ayyoub, Ibrahim
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Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data. [PDF]
Adv Intell DiscovThis article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Ren Y, Wei GW.
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On Monomial Golod Ideals [PDF]
Acta Mathematica Vietnamica, 2020 AbstractWe study ideal-theoretic conditions for a monomial ideal to be Golod. For ideals in a polynomial ring in three variables, our criteria give a complete characterization. Over such rings, we show that the product of two monomial ideals is Golod.
Dao H., De Stefani A.
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Monomial Ideals under Ideal Operations [PDF]
Communications in Algebra, 2015 In this paper, we show for a monomial ideal $I$ of $K[x_1,x_2,\ldots,x_n]$ that the integral closure $\ol{I}$ is a monomial ideal of Borel type (Borel-fixed, strongly stable, lexsegment, or universal lexsegment respectively), if $I$ has the same property.
Guo, Jin, Wu, Tongsuo
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Some counterexamples for (strong) persistence property and (nearly) normally torsion-freeness
Examples and Counterexamples, 2023 In this article, we present some rare counterexamples, which are related to (strong) persistence property and (nearly) normally torsion-freeness of monomial ideals.
Mehrdad Nasernejad
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Monomial s-sequences arising from graph ideals
Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali, 2023 Ideals arising from graphs are investigated via s-sequence theory. In particular, the notion of s-sequence for the generators of the edge ideal I(G) of an acyclic graph G is considered for describing the Groebner basis of the relation ideal J of the ...
Maurizio Imbesi, Monica La Barbiera
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Klyachko Diagrams of Monomial Ideals
Algebras and Representation Theory, 2022 AbstractIn this paper, we introduce the notion of a Klyachko diagram for a monomial ideal I in a certain multi-graded polynomial ring, namely the Cox ring R of a smooth complete toric variety, with irrelevant maximal ideal B. We present procedures to compute the Klyachko diagram of I from its monomial generators, and to retrieve the B −saturation Isat ...
Rosa M. Miró-Roig, Marti Salat-Moltó
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Products of ideals may not be Golod [PDF]
, 2016 We exhibit an example of a product of two proper monomial ideals such that the residue class ring is not Golod. We also discuss the strongly Golod property for rational powers of monomial ideals, and introduce some sufficient conditions for weak ...
De Stefani, Alessandro
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Monomial difference ideals [PDF]
Proceedings of the American Mathematical Society, 2016 In this paper, basic properties of monomial difference ideals are studied. We prove the finitely generated property of well-mixed difference ideals generated by monomials. Furthermore, a finite prime decomposition of radical well-mixed monomial difference ideals is given.
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