The group ring of Richard Thompson’s Group has no minimal non-zero ideals
John Donnelly (2019)
Archivum Mathematicum
Similarity:
We use a total order on Thompson’s group to show that the group ring has no minimal non-zero ideals.
John Donnelly (2019)
Archivum Mathematicum
Similarity:
We use a total order on Thompson’s group to show that the group ring has no minimal non-zero ideals.
Emel Aslankarayiğit Uğurlu, El Mehdi Bouba, Ünsal Tekir, Suat Koç (2023)
Czechoslovak Mathematical Journal
Similarity:
We introduce weakly strongly quasi-primary (briefly, wsq-primary) ideals in commutative rings. Let be a commutative ring with a nonzero identity and a proper ideal of . The proper ideal is said to be a weakly strongly quasi-primary ideal if whenever for some , then or Many examples and properties of wsq-primary ideals are given. Also, we characterize nonlocal Noetherian von Neumann regular rings, fields, nonlocal rings over which every proper ideal is wsq-primary, and zero...
Ibrahim Al-Ayyoub, Mehrdad Nasernejad (2021)
Czechoslovak Mathematical Journal
Similarity:
We provide a construction of monomial ideals in such that , where denotes the least number of generators. This construction generalizes the main result of S. Eliahou, J. Herzog, M. Mohammadi Saem (2018). Working in the ring , we generalize the definition of a Freiman ideal which was introduced in J. Herzog, G. Zhu (2019) and then we give a complete characterization of such ideals. A particular case of this characterization leads to some further investigations on that generalize...
Taras Banakh, Volodymyr Gavrylkiv
Similarity:
Given a group X we study the algebraic structure of the compact right-topological semigroup λ(X) consisting of all maximal linked systems on X. This semigroup contains the semigroup β(X) of ultrafilters as a closed subsemigroup. We construct a faithful representation of the semigroup λ(X) in the semigroup of all self-maps of the power-set (X) and show that the image of λ(X) in coincides with the semigroup of all functions f: (X) → (X) that are equivariant, monotone and symmetric...
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...
B. Sari, Th. Schlumprecht, N. Tomczak-Jaegermann, V. G. Troitsky (2007)
Studia Mathematica
Similarity:
It is well known that the only proper non-trivial norm closed ideal in the algebra L(X) for (1 ≤ p < ∞) or X = c₀ is the ideal of compact operators. The next natural question is to describe all closed ideals of for 1 ≤ p,q < ∞, p ≠ q, or equivalently, the closed ideals in for p < q. This paper shows that for 1 < p < 2 < q < ∞ there are at least four distinct proper closed ideals in , including one that has not been studied before. The proofs use various methods...
Pierre Matet (2013)
Fundamenta Mathematicae
Similarity:
We discuss the problem of whether there exists a restriction of the noncofinal ideal on that is normal.
Somayeh Hadjirezaei, Sina Hedayat (2020)
Czechoslovak Mathematical Journal
Similarity:
Let be a commutative Noetherian ring and be a finitely generated -module. The main result of this paper is to characterize modules whose first nonzero Fitting ideal is a product of maximal ideals of , in some cases.
Papa A. Sissokho (2014)
Acta Arithmetica
Similarity:
A zero-sum sequence over ℤ is a sequence with terms in ℤ that sum to 0. It is called minimal if it does not contain a proper zero-sum subsequence. Consider a minimal zero-sum sequence over ℤ with positive terms and negative terms . We prove that h ≤ ⌊σ⁺/k⌋ and k ≤ ⌊σ⁺/h⌋, where . These bounds are tight and improve upon previous results. We also show a natural partial order structure on the collection of all minimal zero-sum sequences over the set i∈ ℤ : -n ≤ i ≤ n for any positive...
Adam Anebri, Najib Mahdou, Emel Aslankarayiğit Uğurlu (2022)
Czechoslovak Mathematical Journal
Similarity:
Let be a commutative ring with a nonzero identity. In this study, we present a new class of ideals lying properly between the class of -ideals and the class of -ideals. A proper ideal of is said to be a quasi -ideal if is an -ideal of Many examples and results are given to disclose the relations between this new concept and others that already exist, namely, the -ideals, the quasi primary ideals, the -ideals and the -ideals. Moreover, we use the quasi -ideals to characterize...
Abdelhafed Elkhadiri, Hassan Sfouli (2006)
Annales Polonici Mathematici
Similarity:
We give some examples of polynomially bounded o-minimal expansions of the ordered field of real numbers where the Weierstrass division theorem does not hold in the ring of germs, at the origin of ℝⁿ, of definable functions.
Khalid A. Mokbel (2015)
Mathematica Bohemica
Similarity:
The concept of -ideals in posets is introduced. Several properties of -ideals in -distributive posets are studied. Characterization of prime ideals to be -ideals in -distributive posets is obtained in terms of minimality of ideals. Further, it is proved that if a prime ideal of a -distributive poset is non-dense, then is an -ideal. Moreover, it is shown that the set of all -ideals of a poset with forms a complete lattice. A result analogous to separation theorem for...
Khalid A. Mokbel (2016)
Mathematica Bohemica
Similarity:
The concept of a -ideal in -distributive posets is introduced. Several properties of -ideals in -distributive posets are established. Further, the interrelationships between -ideals and -ideals in -distributive posets are investigated. Moreover, a characterization of prime ideals to be -ideals in -distributive posets is obtained in terms of non-dense ideals. It is shown that every -ideal of a -distributive meet semilattice is semiprime. Several counterexamples are discussed. ...
Brian Lehmann (2014)
Annales de l’institut Fourier
Similarity:
Given a pseudo-effective divisor we construct the diminished ideal , a “continuous” extension of the asymptotic multiplier ideal for big divisors to the pseudo-effective boundary. Our main theorem shows that for most pseudo-effective divisors the multiplier ideal of the metric of minimal singularities on is contained in . We also characterize abundant divisors using the diminished ideal, indicating that the geometric and analytic information should coincide.