Results 41 to 50 of about 709,548 (225)

ANNIHILATOR OF LOCAL COHOMOLOGY MODULES UNDER THE RING EXTENSION R⊂R[X] [PDF]

Journal of Algebraic Systems, 2020
Let R be a commutative Noetherian ring, I an ideal of R and M a non-zero R-module. In this paper we calculate the extension of annihilator of local cohomology modules H^t_I(M), t≥0, under the ring extension R⊂R[X] (resp. R⊂R[[X]]).
M. Seidali Samani, K. Bahmanpour
doaj   +1 more source

Rings Graded By a Generalized Group

Topological Algebra and its Applications, 2014
The aim of this paper is to consider the ringswhich can be graded by completely simple semigroups.We show that each G-graded ring has an orthonormal basis, where G is a completely simple semigroup. Weprove that if I is a complete homogeneous ideal of a G-
Fatehi Farzad, Molaei Mohammad Reza
doaj   +1 more source

On the properties of weak CM rings

上海师范大学学报. 自然科学版, 2022
In this paper, we mainly study the properties of weak CM rings. It is a special class of Noetherian commutative rings, including Cohen-Macaulay rings, excellent rings and generalized Cohen-Macaulay rings, which can be characterized by local cohomology ...
XUE Wensi, ZHOU Caijun
doaj   +1 more source

A non-Noetherian factorial ring

, 1972
This paper supplies a counterexample to the conjecture that factorial implies Noetherian in finite Krull dimension. The example is the integral closure of a three-dimensional Noetherian ring, and is the union of Noetherian domains, which are proven to be
John David
core   +1 more source

Fuzzy k-Primary Decomposition of Fuzzy k-Ideal in a Semiring

Fuzzy Information and Engineering, 2015
In this paper, we establish that the Lasker–Noether theorem for a commutative ring may be generalized for a commutative semiring. We produce an example of an ideal in a Noetherian semiring which cannot be expressed as finite intersection of primary ...
S. Kar, S. Purkait, B. Davvaz
doaj   +1 more source

Noetherian subsets of prime spectra

, 1983
If X X is a noetherian subspace of Spec R R , the set of primes of R [ x ] R[x] lying over X X is also noetherian. A simple consequence is the theorem of
Charles C. Hanna, Jon L. Johnson
core   +1 more source

Graded Differential Polynomial Rings

Mathematische Nachrichten, EarlyView.
ABSTRACT We study differential polynomial rings R[t;δ]$R[t;\delta]$ over Γ$\Gamma$‐graded rings, where Γ$\Gamma$ is an arbitrary group. We show that R[t;δ]$R[t;\delta]$ admits a Γ$\Gamma$‐grading compatible with that of R$R$ if and only if δ$\delta$ is a γ$\gamma$‐derivation for some γ∈CΓ(ΓR)$\gamma \in C_\Gamma (\Gamma _R)$, and that this grading is ...
Yassine Ait Mohamed
wiley   +1 more source

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
wiley   +1 more source

Invariant algebras and completely reducible representations [PDF]

, 1994
We give a general construction of affine noetherian algebras with the property that every finite dimensional representation is completely reducible. Starting from enveloping algebras of semi simple Lie algebras in characteristic zero we obtain explicit ...
Kraft, Hanspeter, Small, Lance W.
core  

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
wiley   +1 more source