Displaying similar documents to “Two remarks on the maximal-ideal space of H

Normal restrictions of the noncofinal ideal on

Pierre Matet (2013)

Fundamenta Mathematicae

Similarity:

We discuss the problem of whether there exists a restriction of the noncofinal ideal on that is normal.

On the ideal class groups of the maximal real subfields of number fields with all roots of unity

Masato Kurihara (1999)

Journal of the European Mathematical Society

Similarity:

In this paper, for a totally real number field we show the ideal class group of is trivial. We also study the -component of the ideal class group of the cyclotomic -extension.

Corrigendum to “Commutators on ” (Studia Math. 206 (2011), 175-190)

Dongyang Chen, William B. Johnson, Bentuo Zheng (2014)

Studia Mathematica

Similarity:

We give a corrected proof of Theorem 2.10 in our paper “Commutators on ” [Studia Math. 206 (2011), 175-190] for the case 1 < q < p < ∞. The case when 1 = q < p < ∞ remains open. As a consequence, the Main Theorem and Corollary 2.17 in that paper are only valid for 1 < p,q < ∞.

C(X) vs. C(X) modulo its socle

F. Azarpanah, O. A. S. Karamzadeh, S. Rahmati (2008)

Colloquium Mathematicae

Similarity:

Let be the socle of C(X). It is shown that each prime ideal in is essential. For each h ∈ C(X), we prove that every prime ideal (resp. z-ideal) of C(X)/(h) is essential if and only if the set Z(h) of zeros of h contains no isolated points (resp. int Z(h) = ∅). It is proved that , where dim C(X) denotes the Goldie dimension of C(X), and the inequality may be strict. We also give an algebraic characterization of compact spaces with at most a countable number of nonisolated points....

On the Noether exponent

Anna Stasica (2003)

Annales Polonici Mathematici

Similarity:

We obtain, in a simple way, an estimate for the Noether exponent of an ideal I without embedded components (i.e. we estimate the smallest number μ such that ).

Duality of measures of non-𝒜-compactness

Juan Manuel Delgado, Cándido Piñeiro (2015)

Studia Mathematica

Similarity:

Let be a Banach operator ideal. Based on the notion of -compactness in a Banach space due to Carl and Stephani, we deal with the notion of measure of non–compactness of an operator. We consider a map (respectively, ) acting on the operators of the surjective (respectively, injective) hull of such that (respectively, ) if and only if the operator T is -compact (respectively, injectively -compact). Under certain conditions on the ideal , we prove an equivalence inequality involving...

A co-ideal based identity-summand graph of a commutative semiring

S. Ebrahimi Atani, S. Dolati Pish Hesari, M. Khoramdel (2015)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let be a strong co-ideal of a commutative semiring with identity. Let be a graph with the set of vertices for some , where two distinct vertices and are adjacent if and only if . We look at the diameter and girth of this graph. Also we discuss when is bipartite. Moreover, studies are done on the planarity, clique, and chromatic number of this graph. Examples illustrating the results are presented.

Eigenspaces of the ideal class group

Cornelius Greither, Radan Kučera (2014)

Annales de l’institut Fourier

Similarity:

The aim of this paper is to prove an analog of Gras’ conjecture for an abelian field and an odd prime dividing the degree assuming that the -part of group is cyclic.

Calculation of the avoiding ideal for

Tamás Terpai (2009)

Banach Center Publications

Similarity:

We calculate the mapping and obtain a generating system of its kernel. As a corollary, bounds on the codimension of fold maps from real projective spaces to Euclidean space are calculated and the rank of a singular bordism group is determined.

Commutators on

Dongyang Chen, William B. Johnson, Bentuo Zheng (2011)

Studia Mathematica

Similarity:

Let T be a bounded linear operator on with 1 ≤ q < ∞ and 1 < p < ∞. Then T is a commutator if and only if for all non-zero λ ∈ ℂ, the operator T - λI is not X-strictly singular.

Ideals in big Lipschitz algebras of analytic functions

Thomas Vils Pedersen (2004)

Studia Mathematica

Similarity:

For 0 < γ ≤ 1, let be the big Lipschitz algebra of functions analytic on the open unit disc which satisfy a Lipschitz condition of order γ on ̅. For a closed set E on the unit circle and an inner function Q, let be the closed ideal in consisting of those functions for which (i) f = 0 on E, (ii) as d(z,E),d(w,E) → 0, (iii) . Also, for a closed ideal I in , let = z ∈ : f(z) = 0 for every f ∈ I and let be the greatest common divisor of the inner parts of non-zero functions...

More remarks on the intersection ideal

Tomasz Weiss (2018)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We prove in ZFC that every additive set is additive, thus we solve Problem 20 from paper [Weiss T., A note on the intersection ideal , Comment. Math. Univ. Carolin. 54 (2013), no. 3, 437-445] in the negative.

Semi -ideals of commutative rings

Ece Yetkin Çelikel, Hani A. Khashan (2022)

Czechoslovak Mathematical Journal

Similarity:

Let be a commutative ring with identity. A proper ideal is said to be an -ideal of if for , and imply . We give a new generalization of the concept of -ideals by defining a proper ideal of to be a semi -ideal if whenever is such that , then or . We give some examples of semi -ideal and investigate semi -ideals under various contexts of constructions such as direct products, homomorphic images and localizations. We present various characterizations of this new...

The strong persistence property and symbolic strong persistence property

Mehrdad Nasernejad, Kazem Khashyarmanesh, Leslie G. Roberts, Jonathan Toledo (2022)

Czechoslovak Mathematical Journal

Similarity:

Let be an ideal in a commutative Noetherian ring . Then the ideal has the strong persistence property if and only if for all , and has the symbolic strong persistence property if and only if for all , where denotes the th symbolic power of . We study the strong persistence property for some classes of monomial ideals. In particular, we present a family of primary monomial ideals failing the strong persistence property. Finally, we show that every square-free monomial...

More on the strongly 1-absorbing primary ideals of commutative rings

Ali Yassine, Mohammad Javad Nikmehr, Reza Nikandish (2024)

Czechoslovak Mathematical Journal

Similarity:

Let be a commutative ring with identity. We study the concept of strongly 1-absorbing primary ideals which is a generalization of -ideals and a subclass of -absorbing primary ideals. A proper ideal of is called strongly 1-absorbing primary if for all nonunit elements such that , it is either or . Some properties of strongly 1-absorbing primary ideals are studied. Finally, rings over which every semi-primary ideal is strongly 1-absorbing primary, and rings over which...

On the regularity and defect sequence of monomial and binomial ideals

Keivan Borna, Abolfazl Mohajer (2019)

Czechoslovak Mathematical Journal

Similarity:

When is a polynomial ring or more generally a standard graded algebra over a field , with homogeneous maximal ideal , it is known that for an ideal of , the regularity of powers of becomes eventually a linear function, i.e., for and some integers , . This motivates writing for every . The sequence , called the of the ideal , is the subject of much research and its nature is still widely unexplored. We know that is eventually constant. In this article, after proving...