Results 11 to 20 of about 111 (101)
Flat modules over commutative noetherian rings [PDF]
Transactions of the American Mathematical Society, 1970 In this work we study flat modules over commutative noetherian rings under two kinds of restriction: that the modules are either submodules of free modules or that they have finite rank. The first ones have nicely behaved annihilators: they are generated by idempotents.
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Asymptotic behaviour of ideals relative to injective modules over commutative Noetherian rings II [PDF]
Proceedings of the Edinburgh Mathematical Society, 1991 Let E be an injective module over a commutative Noetherian ring A (with non-zero identity), and let a be an ideal of A. The submodule (0:Eα) of E has a secondary representation, and so we can form the finite set AttA(0:Eα) of its attached prime ideals.
Toroghy, H. Ansari, Sharp, R. Y.
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Classifying subcategories of modules over a commutative noetherian ring [PDF]
Journal of the London Mathematical Society, 2008 Let R be a quotient ring of a commutative coherent regular ring by a finitely generated ideal. Hovey gave a bijection between the set of coherent subcategories of the category of finitely presented R-modules and the set of thick subcategories of the derived category of perfect R-complexes.
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ON THE PRIME SPECTRUM OF A MODULE OVER A COMMUTATIVE NOETHERIAN RING
Honam Mathematical Journal, 2007 Let R be a commutative ring and let M be an R-module. Let X = Spec(M) be the prime spectrum of M with Zariski topology. Our main purpose in this paper is to specify the topological dimensions of X, where X is a Noetherian topological space, and compare them with those of topological dimensions of (M).
H. Ansari-Toroghy, R. Sarmazdeh-Ovlyaee
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Noetherian PI Rings not Module-Finite Over any Commutative Subring [PDF]
Proceedings of the American Mathematical Society, 1982 We construct a ring R R of 3 × 3 3 \times 3 matrices over k [ x , y , z ] k[x,y,z] which is prime, affine, Noetherian, and PI, but not finitely generated as a module nor integral over any commutative subring.
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Infinity‐operadic foundations for embedding calculus
Journal of Topology, Volume 19, Issue 2, June 2026.Abstract Motivated by applications to spaces of embeddings and automorphisms of manifolds, we consider a tower of ∞$\infty$‐categories of truncated right modules over a unital ∞$\infty$‐operad O$\mathcal {O}$. We study monoidality and naturality properties of this tower, identify its layers, describe the difference between the towers as O$\mathcal {O}$
Manuel Krannich, Alexander Kupers
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Counting submodules of a module over a noetherian commutative ring
Journal of Algebra, 2019 We count the number of submodules of an arbitrary module over a countable noetherian commutative ring. We give, along the way, a structural description of meager modules, which are defined as those that do not have the square of a simple module as subquotient.
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Measuring birational derived splinters
Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.Abstract This work is concerned with categorical methods for studying singularities. Our focus is on birational derived splinters, which is a notion that extends the definition of rational singularities beyond varieties over fields of characteristic zero. Particularly, we show that an invariant called ‘level’ in the associated derived category measures
Timothy De Deyn +3 more
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Secondary representations for injective modules over commutative Noetherian rings [PDF]
Proceedings of the Edinburgh Mathematical Society, 1976 There have been several recent accounts of a theory dual to the well-known theory of primary decomposition for modules over a (non-trivial) commutative ring A with identity: see (4), (2) and (9). Here we shall follow Macdonald's terminology from (4) and refer to this dual theory as “ secondary representation theory ”.
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A classification of Prüfer domains of integer‐valued polynomials on algebras
Bulletin of the London Mathematical Society, Volume 58, Issue 4, April 2026.Abstract Let D$D$ be an integrally closed domain with quotient field K$K$ and A$A$ a torsion‐free D$D$‐algebra that is finitely generated as a D$D$‐module and such that A∩K=D$A\cap K=D$. We give a complete classification of those D$D$ and A$A$ for which the ring IntK(A)={f∈K[X]∣f(A)⊆A}$\textnormal {Int}_K(A)=\lbrace f\in K[X] \mid f(A)\subseteq A ...
Giulio Peruginelli, Nicholas J. Werner
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