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22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007), 2007
A topological space is Noetherian iff every open is compact. Our starting point is that this notion generalizes that of well-quasi order, in the sense that an Alexandroff-discrete space is Noetherian iff its specialization quasi-ordering is well. For more general spaces, this opens the way to verifying infinite transition systems based on non-well ...
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A topological space is Noetherian iff every open is compact. Our starting point is that this notion generalizes that of well-quasi order, in the sense that an Alexandroff-discrete space is Noetherian iff its specialization quasi-ordering is well. For more general spaces, this opens the way to verifying infinite transition systems based on non-well ...
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Communications in Algebra, 1976
Kaplansky asked if in a Noetherian domain the intersection of two height 2 primes must contain a non-zero prime. This paper presents a counterexample. Some positive results are given in [2]. The construction in the example proper considerably simpli-fies the argument of [3-Theorem 2.5]. We assume familiarity with [1, Section 1-5].
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Kaplansky asked if in a Noetherian domain the intersection of two height 2 primes must contain a non-zero prime. This paper presents a counterexample. Some positive results are given in [2]. The construction in the example proper considerably simpli-fies the argument of [3-Theorem 2.5]. We assume familiarity with [1, Section 1-5].
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commutative algebra noetherian and non noetherian perspectives
2011- Introduction.- 1. Principal-like Ideals and Related Polynomial Content Conditions (D.D. Anderson).- 2. Zero-divisor Graphs in Commutative Rings (D.F. Anderson, M. Axtell, J. Stickles).- 3. Class Semigroups and T-class Semigroups of Domains (S. Bazzoni, S. Kabbaj).- 4. Forcing Algebras, Syzygy Bundles, and Tight Closure (H. Brenner).- 5.
FONTANA, Marco +3 more
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Do Noetherian Modules Have Noetherian Basis Functions?
2006In Bishop-style constructive algebra it is known that if a module over a commutative ring has a Noetherian basis function, then it is Noetherian. Using countable choice we prove the reverse implication for countable and strongly discrete modules. The Hilbert basis theorem for this specific class of Noetherian modules, and polynomials in a single ...
Júlia Zappe, Peter Schuster
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Communications in Algebra, 2002
ABSTRACT A commutative ring R with identity is called S-Noetherian, where is a given multiplicative set, if for each ideal I of R, for some and some finitely generated ideal J. Using this concept, we tie together several different known results. For instance, the fact that is a Noetherian ring whenever R is so, and that is Noetherian whenever for each ...
D. D. Anderson, Tiberiu Dumitrescu
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ABSTRACT A commutative ring R with identity is called S-Noetherian, where is a given multiplicative set, if for each ideal I of R, for some and some finitely generated ideal J. Using this concept, we tie together several different known results. For instance, the fact that is a Noetherian ring whenever R is so, and that is Noetherian whenever for each ...
D. D. Anderson, Tiberiu Dumitrescu
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Noetherian pairs and hereditarily Noetherian rings
Archiv der Mathematik, 1983William Heinzer, Robert Gilmer
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