Results 31 to 40 of about 482,834 (118)

Some Properties of Serre Subcategories in the Graded Local Cohomology Modules

Journal of Mathematics, Volume 2017, Issue 1, 2017., 2017
Let R = ⊕n≥0Rn be a standard homogeneous Noetherian ring with local base ring (R0,m0) and let M be a finitely generated graded R‐module. Let HR+i(M) be the ith local cohomology module of M with respect to R+ = ⊕n>0Rn. Let S be a Serre subcategory of the category of R‐modules and let i be a nonnegative integer.
Feysal Hassani, Rasul Rasuli, Ali Jaballah   +2 more
wiley   +1 more source

Ideal‐Driven βθ‐I‐Open Sets and Their Role in Connectedness, Hyperconnectedness, and Extremal Disconnectedness

Journal of Mathematics, Volume 2026, Issue 1, 2026.
In this paper, we introduce a novel type of open set, called βθ−I‐open sets, constructed by means of an ideal on a topological space. These sets broaden the classical definition of openness. Employing these ideal‐based generalized open sets, we investigate essential topological properties—including connectedness, hyperconnectedness, and extremal ...
Naeem Nisar Sheikh, Chawalit Boonpok, Areeyuth Sama-Ae, Meltem Sertbaş   +3 more
wiley   +1 more source

Generalized ⊕‐Radical Supplemented Modules

International Scholarly Research Notices, Volume 2014, Issue 1, 2014., 2014
Çalışıcı and Türkmen called a module M generalized ⊕‐supplemented if every submodule has a generalized supplement that is a direct summand of M. Motivated by this, it is natural to introduce another notion that we called generalized ⊕‐radical supplemented modules as a proper generalization of generalized ⊕‐supplemented modules. In this paper, we obtain
Burcu Nişancı Türkmen, Ali Pancar, A. V. Kelarev, S. Yang   +3 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

Cohomological dimension, cofiniteness and Abelian categories of cofinite modules

Journal of Algebra, 2017
Let $R$ be a commutative Noetherian ring, $I$ be an ideal of $R$, and $M$ be an $R$-module. Recall that, the notion of the cohomological dimension of $M$ relative to $I$, denoted by $\mathrm{cd}(I,M)$, is defined to be the greatest integer $i$ such that $H_I^i(M)\neq 0$ if there exist such $i$'s and $-infty$ otherwise.
openaire   +2 more sources

On cofinitely weak rad-supplemented modules

Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, 2017
In this paper, necessary and sufficient conditions for a quotient module are found to be a cofinitely weak Rad-supplemented module under which circumstances. Nevertheless, some relations are investigated between cofinitely Rad-supplemented modules and cofinitely weak Rad-supplemented modules.
ERYILMAZ, Figen, EREN, Şenol
openaire   +2 more sources

Cofiniteness of modules and local cohomology

Rendiconti del Circolo Matematico di Palermo Series 2, 2023
Let $A$ be a commutative noetherian ring, let $\mathfrak a$ be an ideal of $A$ and let $n$ be a non-negative integer. In this paper, we study $\mathcal{S}_{n}(\mathfrak{a})$, a certain class of $A$-modules and we find some sufficient conditions so that a module belongs to $\mathcal{S}_{n}(\mathfrak{a})$.
Sabzeh, Hajar, Sazeedeh, Reza
openaire   +3 more sources

The growth of Tate–Shafarevich groups of p$p$‐supersingular elliptic curves over anticyclotomic Zp${\mathbb {Z}}_p$‐extensions at inert primes

Mathematika, Volume 71, Issue 4, October 2025.
Abstract Let E$E$ be an elliptic curve defined over Q${\mathbb {Q}}$, and let K$K$ be an imaginary quadratic field. Consider an odd prime p$p$ at which E$E$ has good supersingular reduction with ap(E)=0$a_p(E)=0$ and which is inert in K$K$. Under the assumption that the signed Selmer groups are cotorsion modules over the corresponding Iwasawa algebra ...
Erman Işik, Antonio Lei
wiley   +1 more source

On Weakly Laskerian and Weakly Cofinite Modules

Algebra Colloquium, 2012
Let R be a commutative Noetherian ring with non-zero identity, 𝔞 an ideal of R and M a finitely generated R-module. We assume that N is a weakly Laskerian R-module and r is a non-negative integer such that the generalized local cohomology module [Formula: see text] is weakly Laskerian for all i < r.
Khashyarmanesh, Kazem, Kosan, M. Tamer, Sahinkaya, Serap   +2 more
openaire   +4 more sources

Algebraic relations between solutions of Painlevé equations

Journal of the London Mathematical Society, Volume 111, Issue 6, June 2025.
Abstract In this manuscript, we make major progress classifying algebraic relations between solutions of Painlevé equations. Our main contribution is to establish the algebraic independence of solutions of various pairs of equations in the Painlevé families; for generic coefficients, we show that all algebraic relations between solutions of equations ...
James Freitag, Joel Nagloo
wiley   +1 more source