Results 21 to 30 of about 811 (133)
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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, 2002 Over the past 25 years, I have been immersed in research in Algebra and more particularly in ring theory. I embarked on writing this book on Smarandache rings (Srings) specially to motivate both ring theorists and Smarandache algebraists to develop and ...
Vasantha, Kandasamy
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Towards the decidability of the theory of modules over finite commutative rings
, 2009 On the basis of the Klingler-Levy classification of finitely generated modules over commutative noetherian rings we approach the old problem of classifying finite commutative rings R with the decidable theory of modules.
PUNINSKI G. +3 more
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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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When are the classes of Gorenstein modules (co)tilting?
Comptes Rendus. MathématiqueFor the class of Gorenstein projective (resp. injective and flat) modules, we investigate and settle the questions when the middle class is tilting and the other ones are cotilting. The applications have in three directions.
Wang, Junpeng +2 more
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Hilbert's Basis Theorem for Poisson Ore Extensions
Mathematische Nachrichten, Volume 299, Issue 11, Page 3464-3470, November 2026.ABSTRACT We prove an analogue of Hilbert's basis theorem for Poisson Ore extensions and Poisson Laurent Ore extensions. We also obtain corresponding results for iterated Poisson Ore extensions and iterated Poisson Laurent Ore extensions associated to commuting Poisson‐pairs.
Per Bäck +3 more
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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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The Boolean spectrum of a Grothendieck category
Journal of the London Mathematical Society, Volume 114, Issue 4, October 2026.Abstract A notion of support for objects in any Grothendieck category is introduced. This is based on the spectral category of a Grothendieck category and uses its Boolean lattice of localising subcategories. The support provides a classification of all subcategories that are closed under arbitrary coproducts, subobjects, and essential extensions ...
Henning Krause
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A Linear Generalization of the Nearly Gorenstein Property, With Applications to Veronese Subalgebras
Mathematische Nachrichten, Volume 299, Issue 9, Page 2436-2451, September 2026.ABSTRACT We study the nearly Gorenstein property for Veronese subalgebras of (semi‐)standard graded algebras. We introduce a condition (♮)$(\natural)$ for Cohen–Macaulay semi‐standard graded rings, motivated by the study of Ehrhart rings. We show that if a semi‐standard graded algebra R$ R$ satisfies (♮)$(\natural)$, then its Veronese subalgebras R(k)$
Sora Miyashita
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