Commutative noetherian rings and modules

Results 21 to 30 of about 111 (101)

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 +2 more
doaj +1 more source

Local equivalence and refinements of Rasmussen's s‐invariant

Journal of Topology, Volume 19, Issue 1, March 2026.
Abstract Inspired by the notions of local equivalence in monopole and Heegaard Floer homology, we introduce a version of local equivalence that combines odd Khovanov homology with equivariant even Khovanov homology into an algebraic package called a local even–odd (LEO) triple.
Nathan M. Dunfield, Robert Lipshitz, Dirk Schütz +2 more
wiley +1 more source

Torsion classes of extended Dynkin quivers over commutative rings

Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.
Abstract For a Noetherian R$R$‐algebra Λ$\Lambda$, there is a canonical inclusion torsΛ→∏p∈SpecRtors(κ(p)Λ)$\mathop {\mathsf {tors}}\Lambda \rightarrow \prod _{\mathfrak {p}\in \operatorname{Spec}R}\mathop {\mathsf {tors}}(\kappa (\mathfrak {p})\Lambda)$, and each element in the image satisfies a certain compatibility condition.
Osamu Iyama, Yuta Kimura
wiley +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

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

Cosupport computations for finitely generated modules over commutative noetherian rings [PDF]

Journal of Algebra, 2018
Comments are welcome; some minor changes made throughout the ...
openaire +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 +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 +2 more
wiley +1 more source

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

Classifying thick subcategories over a Koszul complex via the curved BGG correspondence

Journal of the London Mathematical Society, Volume 112, Issue 5, November 2025.
Abstract In this work, we classify the thick subcategories of the bounded derived category of dg modules over a Koszul complex on any list of elements in a regular ring. This simultaneously recovers a theorem of Stevenson when the list of elements is a regular sequence and the classification of thick subcategories for an exterior algebra over a field ...
Jian Liu, Josh Pollitz
wiley +1 more source