Displaying similar documents to “A generalization of semiflows on monomials”

On wsq-primary ideals

Emel Aslankarayiğit Uğurlu, El Mehdi Bouba, Ünsal Tekir, Suat Koç (2023)

Czechoslovak Mathematical Journal

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We introduce weakly strongly quasi-primary (briefly, wsq-primary) ideals in commutative rings. Let R be a commutative ring with a nonzero identity and Q a proper ideal of R . The proper ideal Q is said to be a weakly strongly quasi-primary ideal if whenever 0 a b Q for some a , b R , then a 2 Q or b Q . 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...

Monomial ideals with tiny squares and Freiman ideals

Ibrahim Al-Ayyoub, Mehrdad Nasernejad (2021)

Czechoslovak Mathematical Journal

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We provide a construction of monomial ideals in R = K [ x , y ] such that μ ( I 2 ) < μ ( I ) , where μ 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 R , 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 μ ( I k ) that generalize...

Algebra in the superextensions of twinic groups

Taras Banakh, Volodymyr Gavrylkiv

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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 ( X ) ( X ) of all self-maps of the power-set (X) and show that the image of λ(X) in ( X ) ( X ) coincides with the semigroup E n d λ ( ( X ) ) of all functions f: (X) → (X) that are equivariant, monotone and symmetric...

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

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

Czechoslovak Mathematical Journal

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Let R be a commutative ring with identity. We study the concept of strongly 1-absorbing primary ideals which is a generalization of n -ideals and a subclass of 1 -absorbing primary ideals. A proper ideal I of R is called strongly 1-absorbing primary if for all nonunit elements a , b , c R such that a b c I , it is either a b I or c 0 . Some properties of strongly 1-absorbing primary ideals are studied. Finally, rings R over which every semi-primary ideal is strongly 1-absorbing primary, and rings R over which...

On norm closed ideals in L ( p , q )

B. Sari, Th. Schlumprecht, N. Tomczak-Jaegermann, V. G. Troitsky (2007)

Studia Mathematica

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It is well known that the only proper non-trivial norm closed ideal in the algebra L(X) for X = p (1 ≤ p < ∞) or X = c₀ is the ideal of compact operators. The next natural question is to describe all closed ideals of L ( p q ) for 1 ≤ p,q < ∞, p ≠ q, or equivalently, the closed ideals in L ( p , q ) for p < q. This paper shows that for 1 < p < 2 < q < ∞ there are at least four distinct proper closed ideals in L ( p , q ) , including one that has not been studied before. The proofs use various methods...

Decomposition of finitely generated modules using Fitting ideals

Somayeh Hadjirezaei, Sina Hedayat (2020)

Czechoslovak Mathematical Journal

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Let R be a commutative Noetherian ring and M be a finitely generated R -module. The main result of this paper is to characterize modules whose first nonzero Fitting ideal is a product of maximal ideals of R , in some cases.

A note on minimal zero-sum sequences over ℤ

Papa A. Sissokho (2014)

Acta Arithmetica

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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 a , . . . , a h and negative terms b , . . . , b k . We prove that h ≤ ⌊σ⁺/k⌋ and k ≤ ⌊σ⁺/h⌋, where σ = i = 1 h a i = - j = 1 k b j . 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...

On quasi n -ideals of commutative rings

Adam Anebri, Najib Mahdou, Emel Aslankarayiğit Uğurlu (2022)

Czechoslovak Mathematical Journal

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Let R be a commutative ring with a nonzero identity. In this study, we present a new class of ideals lying properly between the class of n -ideals and the class of ( 2 , n ) -ideals. A proper ideal I of R is said to be a quasi n -ideal if I is an n -ideal of R . Many examples and results are given to disclose the relations between this new concept and others that already exist, namely, the n -ideals, the quasi primary ideals, the ( 2 , n ) -ideals and the p r -ideals. Moreover, we use the quasi n -ideals to characterize...

α -ideals in 0 -distributive posets

Khalid A. Mokbel (2015)

Mathematica Bohemica

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The concept of α -ideals in posets is introduced. Several properties of α -ideals in 0 -distributive posets are studied. Characterization of prime ideals to be α -ideals in 0 -distributive posets is obtained in terms of minimality of ideals. Further, it is proved that if a prime ideal I of a 0 -distributive poset is non-dense, then I is an α -ideal. Moreover, it is shown that the set of all α -ideals α Id ( P ) of a poset P with 0 forms a complete lattice. A result analogous to separation theorem for...

0 -ideals in 0 -distributive posets

Khalid A. Mokbel (2016)

Mathematica Bohemica

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The concept of a 0 -ideal in 0 -distributive posets is introduced. Several properties of 0 -ideals in 0 -distributive posets are established. Further, the interrelationships between 0 -ideals and α -ideals in 0 -distributive posets are investigated. Moreover, a characterization of prime ideals to be 0 -ideals in 0 -distributive posets is obtained in terms of non-dense ideals. It is shown that every 0 -ideal of a 0 -distributive meet semilattice is semiprime. Several counterexamples are discussed. ...

Algebraic bounds on analytic multiplier ideals

Brian Lehmann (2014)

Annales de l’institut Fourier

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Given a pseudo-effective divisor L we construct the diminished ideal 𝒥 σ ( L ) , 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 L the multiplier ideal 𝒥 ( h min ) of the metric of minimal singularities on 𝒪 X ( L ) is contained in 𝒥 σ ( L ) . We also characterize abundant divisors using the diminished ideal, indicating that the geometric and analytic information should coincide.