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Let $K$ be a field and $S = K [x_{1}, ..., x_{n}]$ . Let $I$ be a monomial ideal of $S$ and $u_{1}, ..., u_{r}$ be monomials in $S$ . We prove that if $u_{1}, ..., u_{r}$ form a filter-regular sequence on $S / I$ , then $S / I$ is pretty clean if and only if $S / (I, u_{1}, ..., u_{r})$ is pretty clean. Also, we show that if $u_{1}, ..., u_{r}$ form a filter-regular sequence on $S / I$ , then Stanley’s conjecture is true for $S / I$ if and only if it is true for $S / (I, u_{1}, ..., u_{r})$ . Finally, we prove that if $u_{1}, ..., u_{r}$ is a minimal set of generators for $I$ which form either a $d$ -sequence, proper sequence or strong $s$ -sequence (with respect to the reverse lexicographic...

Primary decomposition of modules over Dedekind domains using Gröbner bases.

Lezama, Oswaldo, Suárez, Héctor (2007)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

Primary decomposition of torsion $R [X]$ -modules.

Adkins, William A. (1994)

International Journal of Mathematics and Mathematical Sciences

Primary ideals with finitely generated radical in a commutative ring.

Robert Gilmer, William Heinzer (1993)

Manuscripta mathematica

Principal ideal theorems for holomorphy rings in fields.

Peter Roquette (1973)

Journal für die reine und angewandte Mathematik

Product formulas for resultants and Chow forms.

Bernd Sturmfels, Paul Pedersen (1993)

Mathematische Zeitschrift

Projective modules and approximation couples

V. K. Grover, N. Sankaran (1990)

Compositio Mathematica

Projective modules over real affine algebras.

R. Parimala, M. Ojanguren (1990)

Mathematische Annalen

Projektive Moduln über Polynomringen A[t1,...,Tm] mit einem regulären Grundring A.

Hartmut Lindel (1977/1978)

Manuscripta mathematica

Propriété d'approximation pour les éléments algébriques

P. Robba (1987)

Compositio Mathematica

Proximity relations for real rank one valuations dominating a local regular ring.

Angel Granja, Cristina Rodríguez (2003)

Revista Matemática Iberoamericana

We study 0-dimensional real rank one valuations centered in a regular local ring of dimension n > 2 such that the associated valuation ring can be obtained from the regular ring by a sequence of quadratic transforms. We define two classical invariants associated to the valuation (the refined proximity matrix and the multiplicity sequence) and we show that are equivalent data of the valuation.

The concept of a Prüfer ring is studied in the case of rings with involution such that it coincides with the corresponding notion in the case of commutative rings.

Pseudobetragsfunktionen auf Quotientenkörpern von Dedekindringen.

K. Kiyek (1975)

Journal für die reine und angewandte Mathematik

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Displaying 21 – 40 of 42

Porjective Modules over Polynomial Rings.

Positivity in coefficient-free rank two cluster algebras.

Positivity of the $T$ -system cluster algebra.

Potenzreihenerweiterung und formale Fasern in lokalen Ringen mit Approximationseigenschaft.

Preservation of the properties of the polynomial ring of the power series ring in the class of finite conductor rings.

Pretty cleanness and filter-regular sequences