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Commutative Algebra I
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A compilation of two sets of notes at the University of Kansas was published in the Spring of 2002 by?? and the other in the spring of 2007 by Branden Stone.Abstract:
1 A compilation of two sets of notes at the University of Kansas; one in the Spring of 2002 by ?? and the other in the Spring of 2007 by Branden Stone. These notes have been typedread more
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Irreducible Jacobian derivations in positive characteristic
TL;DR: In this paper, it was shown that an irreducible polynomial derivation in positive characteristic is a Jacobian derivation if and only if there exists an n-1-element p-basis of its ring of constants.
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K + M constructions with general overrings and relationships with polynomial composites
TL;DR: In this article, the authors considered the construction of polynomial composites, where K is the domain, M is the maximal ideal of a polynomials with coefficients from the field L, and K is its subring.
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Counting Real Roots in Polynomial-Time via Diophantine Approximation
TL;DR: In this article , the authors gave an algorithm that, for any fixed n, counts exactly the number of real roots of F in time polynomial in (log(d)H)H.
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Lefschetz properties of monomial algebras with almost linear resolution
Nasrin Altafi,Navid Nemati +1 more
TL;DR: In this paper, the WLP and SLP of artinian monomial ideals in S = K[x1, 1, n] were studied via studying their minimal free resolutions.
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On the notion of sequentially Cohen–Macaulay modules
TL;DR: In this article , the main properties of sequential Cohen-Macaulay modules are presented and some basic examples are provided to help the reader with quickly getting acquainted with this topic, and two generalizations of the notion of sequential MC are discussed, inspired by a theorem of Jurgen Herzog and the third author.
References
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Book
Introduction to Commutative Algebra
TL;DR: It is shown here how the Noetherian Rings and Dedekind Domains can be transformed into rings and Modules of Fractions using the following structures: