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Monomial ideals with 3-linear resolutions

Marcel Morales, Abbas Nasrollah Nejad, Ali Akbar Yazdan Pour, Rashid Zaare-Nahandi (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

In this paper, we study the Castelnuovo-Mumford regularity of square-free monomial ideals generated in degree 3 . We define some operations on the clutters associated to such ideals and prove that the regularity is preserved under these operations. We apply these operations to introduce some classes of ideals with linear resolutions and also show that any clutter corresponding to a triangulation of the sphere does not have linear resolution while any proper subclutter of it has a linear resolution....

Monomial ideals with tiny squares and Freiman ideals

Ibrahim Al-Ayyoub, Mehrdad Nasernejad (2021)

Czechoslovak Mathematical Journal

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 some results...

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

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

Czechoslovak Mathematical Journal

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 every strongly...

Multigraded modules.

Charalambous, Hara, Deno, Christa (2001)

The New York Journal of Mathematics [electronic only]

Multiplication modules and related results

Shahabaddin Ebrahimi Atani (2004)

Archivum Mathematicum

Let R be a commutative ring with non-zero identity. Various properties of multiplication modules are considered. We generalize Ohm’s properties for submodules of a finitely generated faithful multiplication R -module (see [8], [12] and [3]).

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