$\alpha $-filters and $\alpha $-order-ideals in distributive quasicomplemented semilattices

Ismael Calomino; Sergio A. Celani

Displaying similar documents to “ $α$ -filters and $α$ -order-ideals in distributive quasicomplemented semilattices”

$0$ -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. ...

$α$ -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...

Semiproper ideals

Hiroshi Sakai (2005)

Fundamenta Mathematicae

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We say that an ideal I on $_{κ} λ$ is semiproper if the corresponding poset $ℙ_{I}$ is semiproper. In this paper we investigate properties of semiproper ideals on $_{κ} λ$ .

On norm closed ideals in $L (ℓ_{p}, ℓ_{q})$

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 $X = ℓ_{p}$ (1 ≤ p < ∞) or X = c₀ is the ideal of compact operators. The next natural question is to describe all closed ideals of $L (ℓ_{p} \oplus ℓ_{q})$ for 1 ≤ p,q < ∞, p ≠ q, or equivalently, the closed ideals in $L (ℓ_{p}, ℓ_{q})$ for p < q. This paper shows that for 1 < p < 2 < q < ∞ there are at least four distinct proper closed ideals in $L (ℓ_{p}, ℓ_{q})$ , including one that has not been studied before. The proofs use various methods...

$(δ, 2)$ -primary ideals of a commutative ring

Gülşen Ulucak, Ece Yetkin Çelikel (2020)

Czechoslovak Mathematical Journal

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Let $R$ be a commutative ring with nonzero identity, let $ℐ (ℛ)$ be the set of all ideals of $R$ and $δ : ℐ (ℛ) \to ℐ (ℛ)$ an expansion of ideals of $R$ defined by $I \mapsto δ (I)$ . We introduce the concept of $(δ, 2)$ -primary ideals in commutative rings. A proper ideal $I$ of $R$ is called a $(δ, 2)$ -primary ideal if whenever $a, b \in R$ and $a b \in I$ , then $a^{2} \in I$ or $b^{2} \in δ (I)$ . Our purpose is to extend the concept of $2$ -ideals to $(δ, 2)$ -primary ideals of commutative rings. Then we investigate the basic properties of $(δ, 2)$ -primary ideals and also discuss the relations among $(δ, 2)$ -primary, $δ$ -primary...

On domains with ACC on invertible ideals

Stefania Gabelli (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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If $A$ is a domain with the ascending chain condition on (integral) invertible ideals, then the group $I(A)$ of its invertible ideals is generated by the set $I_{m}(A)$ of maximal invertible ideals. In this note we study some properties of $I_{m}(A)$ and we prove that, if $I(A)$ is a free group on $I_{m}(A)$ , then $A$ is a locally factorial Krull domain.

On the mappings $𝒵_{A}$ and $ℑ_{A}$ in intermediate rings of $C (X)$

Mehdi Parsinia (2018)

Commentationes Mathematicae Universitatis Carolinae

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In this article, we investigate new topological descriptions for two well-known mappings $𝒵_{A}$ and $ℑ_{A}$ defined on intermediate rings $A (X)$ of $C (X)$ . Using this, coincidence of each two classes of $z$ -ideals, $𝒵_{A}$ -ideals and $ℑ_{A}$ -ideals of $A (X)$ is studied. Moreover, we answer five questions concerning the mapping $ℑ_{A}$ raised in [J. Sack, S. Watson, $C$ and $C^{*}$ among intermediate rings, Topology Proc. 43 (2014), 69–82].

The graphs of join-semilattices and the shape of congruence lattices of particle lattices

Pavel Růžička (2017)

Commentationes Mathematicae Universitatis Carolinae

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We attach to each $〈 0, \lor 〉$ -semilattice $S$ a graph $G_{S}$ whose vertices are join-irreducible elements of $S$ and whose edges correspond to the reflexive dependency relation. We study properties of the graph $G_{S}$ both when $S$ is a join-semilattice and when it is a lattice. We call a $〈 0, \lor 〉$ -semilattice $S$ particle provided that the set of its join-irreducible elements satisfies DCC and join-generates $S$ . We prove that the congruence lattice of a particle lattice is anti-isomorphic to the lattice of all hereditary...

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 $\sqrt{I}$ 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...

Effective Nullstellensatz for arbitrary ideals

János Kollár (1999)

Journal of the European Mathematical Society

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Let $f_{i}$ be polynomials in $n$ variables without a common zero. Hilbert’s Nullstellensatz says that there are polynomials $g_{i}$ such that $\sum g_{i} f_{i} = 1$ . The effective versions of this result bound the degrees of the $g_{i}$ in terms of the degrees of the $f_{j}$ . The aim of this paper is to generalize this to the case when the $f_{i}$ are replaced by arbitrary ideals. Applications to the Bézout theorem, to Łojasiewicz–type inequalities and to deformation theory are also discussed.

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...

$G r$ - $(2, n)$ -ideals in graded commutative rings

Khaldoun Al-Zoubi, Shatha Alghueiri, Ece Y. Celikel (2020)

Commentationes Mathematicae Universitatis Carolinae

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Let $G$ be a group with identity $e$ and let $R$ be a $G$ -graded ring. In this paper, we introduce and study the concept of graded $(2, n)$ -ideals of $R$ . A proper graded ideal $I$ of $R$ is called a graded $(2, n)$ -ideal of $R$ if whenever $r s t \in I$ where $r, s, t \in h (R)$ , then either $r t \in I$ or $r s \in G r (0)$ or $s t \in G r (0)$ . We introduce several results concerning $g r$ - $(2, n)$ -ideals. For example, we give a characterization of graded $(2, n)$ -ideals and their homogeneous components. Also, the relations between graded $(2, n)$ -ideals and others that already exist, namely, the graded prime...

Fixed points with respect to the L-slice homomorphism $σ_{a}$

K.S. Sabna, N.R. Mangalambal (2019)

Archivum Mathematicum

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Given a locale $L$ and a join semilattice $J$ with bottom element $0_{J}$ , a new concept $(σ, J)$ called $L$ -slice is defined,where $σ$ is as an action of the locale $L$ on the join semilattice $J$ . The $L$ -slice $(σ, J)$ adopts topological properties of the locale $L$ through the action $σ$ . It is shown that for each $a \in L$ , $σ_{a}$ is an interior operator on $(σ, J)$ .The collection $M = {σ_{a}; a \in L}$ is a Priestly space and a subslice of $L$ - $Hom (J, J)$ . If the locale $L$ is spatial we establish an isomorphism between the $L$ -slices $(σ, L)$ and $(δ, M)$ . We have shown that the fixed...

Generalization of the $S$ -Noetherian concept

Abdelamir Dabbabi, Ali Benhissi (2023)

Archivum Mathematicum

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Let $A$ be a commutative ring and $𝒮$ a multiplicative system of ideals. We say that $A$ is $𝒮$ -Noetherian, if for each ideal $Q$ of $A$ , there exist $I \in 𝒮$ and a finitely generated ideal $F \subseteq Q$ such that $I Q \subseteq F$ . In this paper, we study the transfer of this property to the polynomial ring and Nagata’s idealization.

Displaying similar documents to “ α -filters and α -order-ideals in distributive quasicomplemented semilattices”

Displaying similar documents to “ $α$ -filters and $α$ -order-ideals in distributive quasicomplemented semilattices”