scholarly journals Hilbert functions of colored quotient rings and a generalization of the Clements–Lindström theorem

2014 ◽  
Vol 42 (1) ◽  
pp. 1-23
Author(s):  
Kai Fong Ernest Chong
Keyword(s):  
Hilbert Functions ◽  
Quotient Rings ◽  
Lindström Theorem

Centers of maximal quotient rings

1988 ◽  
Vol 50 (4) ◽  
pp. 342-347 ◽  
Author(s):  
Pere Ara
Keyword(s):  
Quotient Rings

scholarly journals Quotient rings of Noetherian module finite rings

1994 ◽  
Vol 121 (2) ◽  
pp. 335-335 ◽  
Author(s):  
A. W. Chatters ◽  
C. R. Hajarnavis
Keyword(s):  
Finite Rings ◽  
Noetherian Module ◽  
Quotient Rings

FINITENESS OF HILBERT FUNCTIONS FOR GENERALIZED COHEN–MACAULAY MODULES

2001 ◽  
Vol 29 (2) ◽  
pp. 805-813 ◽  
Author(s):  
Vijaylaxmi Trivedi
Keyword(s):  
Hilbert Functions

Intersections of quotient rings and Prüfer v-multiplication domains

2016 ◽  
Vol 15 (08) ◽  
pp. 1650149 ◽  
Author(s):  
Said El Baghdadi ◽  
Marco Fontana ◽  
Muhammad Zafrullah
Keyword(s):  
Integral Domain ◽  
Algebraic Approach ◽  
Quotient Field ◽  
Topological Characterization ◽  
Locally Finite ◽  
Star Operation ◽  
Star Operations ◽  
Quotient Rings ◽  
Special Case

Let [Formula: see text] be an integral domain with quotient field [Formula: see text]. Call an overring [Formula: see text] of [Formula: see text] a subring of [Formula: see text] containing [Formula: see text] as a subring. A family [Formula: see text] of overrings of [Formula: see text] is called a defining family of [Formula: see text], if [Formula: see text]. Call an overring [Formula: see text] a sublocalization of [Formula: see text], if [Formula: see text] has a defining family consisting of rings of fractions of [Formula: see text]. Sublocalizations and their intersections exhibit interesting examples of semistar or star operations [D. D. Anderson, Star operations induced by overrings, Comm. Algebra 16 (1988) 2535–2553]. We show as a consequence of our work that domains that are locally finite intersections of Prüfer [Formula: see text]-multiplication (respectively, Mori) sublocalizations turn out to be Prüfer [Formula: see text]-multiplication domains (PvMDs) (respectively, Mori); in particular, for the Mori domain case, we reobtain a special case of Théorème 1 of [J. Querré, Intersections d’anneaux intègers, J. Algebra 43 (1976) 55–60] and Proposition 3.2 of [N. Dessagnes, Intersections d’anneaux de Mori — exemples, Port. Math. 44 (1987) 379–392]. We also show that, more than the finite character of the defining family, it is the finite character of the star operation induced by the defining family that causes the interesting results. As a particular case of this theory, we provide a purely algebraic approach for characterizing P vMDs as a subclass of the class of essential domains (see also Theorem 2.4 of [C. A. Finocchiaro and F. Tartarone, On a topological characterization of Prüfer [Formula: see text]-multiplication domains among essential domains, preprint (2014), arXiv:1410.4037]).

Hilbert functions and the extension functor

1989 ◽  
Vol 105 (3) ◽  
pp. 441-446 ◽  
Author(s):  
David Kirby
Keyword(s):  
Commutative Ring ◽  
Hilbert Functions ◽  
Definition Of

Throughout R will denote a commutative ring with identity, A,B etc. will denote ideals of R, and E will denote a unitary R-module. We recall from [5] the definition of homological grade hgrR(A;E) as inf{r|ExtRr(R/A,E) ≠ 0}, and we allow both hgrR(A;E) = ∞ (i.e. ExtRr(R/A,E) = 0 for all r) and AE = E. For the most part E will be Noetherian, in which case hgrR(A;E) coincides with the usual grade grR(A;E) which is the supremum of the lengths of the (weak) E-sequences contained in A (see [7], for example).

scholarly journals Interval conjectures for level Hilbert functions

2009 ◽  
Vol 321 (10) ◽  
pp. 2705-2715 ◽  
Author(s):  
Fabrizio Zanello
Keyword(s):  
Hilbert Functions

Gröbner bases specialization through Hilbert functions

2000 ◽  
Vol 34 (1) ◽  
pp. 1-8 ◽  
Author(s):  
M.-J. Gonzalez-Lopez ◽  
L. Gonzalez-Vega ◽  
C. Traverso ◽  
A. Zanoni
Keyword(s):  
Gröbner Bases ◽  
Grobner Bases ◽  
Hilbert Functions
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