Results 21 to 30 of about 12,073 (92)

Criteria for flatness and injectivity

, 2011
Let $R$ be a commutative Noetherian ring. We give criteria for flatness of $R$-modules in terms of associated primes and torsion-freeness of certain tensor products.
A.S. Richardson, D. Kirby, E. Kunz, E. Matlis, E. Matlis, H. Zöschinger, I. Kaplansky, I.M. Aberbach, K. Divaani-Aazar, L. Angeleri Hügel, L. Chambless, L. Fuchs, L.L. Avramov, Neil Epstein, R.Y. Sharp, S. Yassemi, S. Yassemi, Yongwei Yao   +17 more
core   +1 more source

Radical preservation and the finitistic dimension

Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.
Abstract We introduce the notion of radical preservation and prove that a radical‐preserving homomorphism of left artinian rings of finite projective dimension with superfluous kernel reflects the finiteness of the little finitistic, big finitistic, and global dimension.
Odysseas Giatagantzidis
wiley   +1 more source

Classes of modules closed under projective covers

Open Mathematics
In this work, we study some classes of modules closed under submodules, quotients, and projective covers, even if the left projective cover of an arbitrary left module not always exists. We obtain a characterization of artinian principal ideal rings when
Cejudo-Castilla César, García-Ramírez Ángel Raúl, Montalvo Ivan Fernando Vilchis   +2 more
doaj   +1 more source

Module structure of Weyl algebras

Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.
Abstract The seminal paper (Stafford, J. Lond. Math. Soc. (2) 18 (1978), no. 3, 429–442) was a major step forward in our understanding of Weyl algebras. Beginning with Serre's Theorem on free summands of projective modules and Bass' Stable Range Theorem in commutative algebra, we attempt to trace the origins of this work and explain how it led to ...
Gwyn Bellamy
wiley   +1 more source

The space of finitely generated rings

, 2009
The space of marked commutative rings on n given generators is a compact metrizable space. We compute the Cantor-Bendixson rank of any member of this space.
Cornulier, Yves
core   +3 more sources

b‐Filter Grade of an Ideal a for Triangulated Categories

Journal of Mathematics, Volume 2026, Issue 1, 2026.
Let a and b be two homogeneous ideals in a graded‐commutative Noetherian ring R, and let X be an object in a compactly generated R‐linear triangulated category T. We introduce the notion of the b‐filter grade of a on X, denoted by f‐gradb,a,X, and provide several characterizations and bounds for this invariant. In addition, we explore the relationships
Li Wang, Hailong Yao, Caihui Lan, Xuexia Dai, Elena Guardo   +4 more
wiley   +1 more source

The shift‐homological spectrum and parametrising kernels of rank functions

Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.
Abstract For any compactly generated triangulated category, we introduce two topological spaces, the shift spectrum and the shift‐homological spectrum. We use them to parametrise a family of thick subcategories of the compact objects, which we call radical.
Isaac Bird, Jordan Williamson, Alexandra Zvonareva   +2 more
wiley   +1 more source

Cohen-Macaulay modules and holonomic modules over filtered rings [PDF]

, 2007
We study Gorenstein dimension and grade of a module $M$ over a filtered ring whose assosiated graded ring is a commutative Noetherian ring. An equality or an inequality between these invariants of a filtered module and its associated graded module is the
Miyahara, Hiroki, Nishida, Kenji
core   +2 more sources

Noncommutative curves and noncommutative surfaces

, 2000
In this survey article we describe some geometric results in the theory of noncommutative rings and, more generally, in the theory of abelian categories.
Bergh, M. Van den, Stafford, J. T.
core   +3 more sources

GL‐algebras in positive characteristic II: The polynomial ring

Proceedings of the London Mathematical Society, Volume 131, Issue 6, December 2025.
Abstract We study GL$\mathbf {GL}$‐equivariant modules over the infinite variable polynomial ring S=k[x1,x2,…,xn,…]$S = k[x_1, x_2, \ldots, x_n, \ldots]$ with k$k$ an infinite field of characteristic p>0$p > 0$. We extend many of Sam–Snowden's far‐reaching results from characteristic zero to this setting.
Karthik Ganapathy
wiley   +1 more source