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Modules for which the natural map of the maximal spectrum is surjective

H. Ansari-Toroghy, R. Ovlyaee-Sarmazdeh (2010)

Colloquium Mathematicae

Let R be a commutative ring with identity. The purpose of this paper is to introduce two new classes of modules over R, called Ms modules and fulmaximal modules respectively. The first (resp. second) class contains the family of finitely generated and primeful (resp. finitely generated and multiplication) modules properly. Our concern is to extend some properties of primeful and multiplication modules to these new classes of modules.

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...

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