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Showing 1 to 19 of 19 for “"Noetherian"”.
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The Baer Criterion For Injective Modules Over Noetherian Rings
… modules. Then we considered the case when R is a Noetherian ring. We discovered that in this case we can refine our criteria for testing modules for injectivity.
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Banach algebras on groups and semigroups
… define a Banach algebra to be topologically left Noetherian if every closed left ideal is topologically finitely-generated, and we seek infinitedimensional examples of such algebras. We show that, given a compact group G, the group algebra L 1 pGq is topologically left Noetherian if and only if G …
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Gorenstein Injective Modules
… this to happen. We prove that when the ring R is noetherian and such that every R-module has finite Gorenstein injective dimension, every direct sum of Gorenstein injective modules is still Gorenstein injective.
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Characterizations Of Zero Divisor Graphs Determined By Equivalence Classes Of Zero Divisors
… classes of zero divisors, specifically for a Noetherian ring R. We study the classification of these graphs. Specifically, we add more criteria to the list of characterizations that disqualify a graph as the zero divisor graph of a ring. We also briefly discuss Sage, a mathematical software, …
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On Gorenstein Projective and Gorenstein Flat Modules
… this statement by showing over commutative Noetherian rings of finite Krull dimension, every Gorenstein at module has finite Gorenstein projective dimension. This statement is the Gorenstein counterpart of a famous theorem of Gruson, Jensen, and Raynaud. Using this result we prove that over …
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Motivic integration over nilpotent structures
… from a discrete valuation ring to any complete Noetherian ring with residue field $\kappa$, where $\kappa$ is any field. Schoutens' functorial approach (as opposed to the traditional model theoretic approach) allows for some very general notions of motivic integration. However, the central focus …
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Purity of the stratification by Newton polygons and Frobenius-periodic vector bundles
… says that the family of Newton polygons over a noetherian scheme have a common break point if this is true outside a subscheme of codimension bigger than 1. The proof is similar to the proof of [dJO99, Theorem 4.1]. In the second part, we prove that for every ordinary genus-2 curve X over a …
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Algebraic geometry and representation theory in the Verlinde category
… built out of it, finitely generated algebras are Noetherian, have finitely generated invariants and are finite as a module over their invariants. Subsequently, we use this result to extend some fundamental properties of commutative algebras from the original setting of vector spaces to the more …
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Display structures on de Rham-Witt cohomology
Let $p$ be a prime number and $R$ be a noetherian and $F$-finite ring where $p \in R$ is nilpotent. In this thesis we prove that the crystalline cohomology of a smooth and proper scheme $X$ over $R$ carries a display structure $\underline{P}^l$ if the crystalline cohomology $H^l_{crys}(X,W(R))$ is …
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A Variation on a Theme of Vasconcelos
… independently demonstrated that an ideal I in a Noetherian local ring R is generated by a regular sequence if and only if I/ I2 is free over R/I and pdRI < infinity. In this thesis, we prove that a radical ideal I in an excellent local normal domain is generated by a regular sequence provided R/I …
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Local coherence of hearts in the derived category of a commutative ring
… turned out to be very interesting over a noetherian ring, for they are in bijection with the Thomason filtrations of the prime spectrum. In other words, they are classified by geometric objects, moreover their constituent subcategories have a precise cohomological description. However, if …
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On the theory of Krull rings and injective modules
… theories. We then look at injective modules over Noetherian rings as in MATLIS [1958] and then over KRULL rings as in BECK [1971]. We show that for a KRULL ring there is a torsion theory (N,M) where N is the pseudo-zero modules and M the set of N-torsion-free (BECK calls these co-divisorial) …
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Transcendence degree in power series rings
… related results are given; for example, if D is Noetherian, and if J is a finite ring extension of D, then either J[[X]] and D[[X]] have the same quotient field or the quotient field of J[[X]] has infinite transcendence degree over the quotient field of D[[X]]. An example is given to show that if …
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Some generalizations of injectivity
… and, in consequence, we prove that, for a right Noetherian ring R, an extending right R-module M1 and a semisimple right R-module M2, the right R-module M1 M2 is extending if and only if M2 is M1/Soc(M1)-injective. Chapter 3 deals with the class of self-c-injective modules, that can be …
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Verificación formal en ACL2 del algoritmo de Buchberger
… induced by the ideal and that the reduction is Noetherian with respect to the underlying polynomial ordering. Algorithms for the computation of normal forms are also presented and it is proved that ideals are closed under them. (6) S-polynomials are formalized and it is proved that the reduction …
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An Introduction to Hilbert’s Nullstellensatz: an Insight for the Algebraically Minded
… their proofs. These statements allow us to skip Noetherian and Jacobson rings by finding the necessary conclusions from polynomial rings over fields. This section also includes an existence conclusion that also can be found in other literature under the name of Weak Nullstellensatz. Afterwards, …
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Resolutions mod I, Golod pairs
… In the case when <i>R</i> = (<i>R</i>, m) is a Noetherian local ring and <i>M</i> is a finitely generated <i>R/ I</i> -module, we discuss the minimality of the constructed resolution. If it is minimal we call (<i>M, I</i>) a Golod pair over <i>R</i>. We give a direct proof of a theorem of Levin …