2 citations · 3 across the 6 of their papers we have counts for
7 papers
Principal vector-spread Borel ideals
Marilena Crupi, Antonino Ficarra, Ernesto Lax
We study the class of squarefree principal vector-spread Borel ideals. We compute the minimal primary decomposition of these ideals and thereby we prove that they are sequentially…
A note on the class of sober rings
Saeid Jafari, Ernesto Lax
We study sober rings, a class of commutative rings in which every prime non-maximal ideal is not the intersection of the prime ideals strictly containing it. We establish basic str…
SCMAlgebras: a Macaulay2 package for sequentially Cohen-Macaulayness
Ernesto Lax
We introduce the Macaulay2 package SCMAlgebras. It provides functions for computing the modules of deficiency and the filter ideals, in order to check whether a module or an ideal…
Sequentially Cohen-Macaulay binomial edge ideals
Ernesto Lax, Giancarlo Rinaldo, Francesco Romeo
We prove that wheels and block graphs have sequentially Cohen-Macaulay binomial edge ideals. Moreover, we provide a construction of new families of sequentially Cohen-Macaulay grap…
Matchings, Squarefree Powers and Betti Splittings
Marilena Crupi, Antonino Ficarra, Ernesto Lax
Let be a finite simple graph and let be its edge ideal. In this article, we deeply investigate the squarefree powers of by means of Betti splittings. When is…
Mapping cones of monomial ideals over exterior algebras
Marilena Crupi, Antonino Ficarra, Ernesto Lax
Let be a field, a finite dimensional -vector space and the exterior algebra of . We analyze iterated mapping cone over . If is a monomial ideal of with…
Macaulay's theorem for vector-spread algebras
Marilena Crupi, Antonino Ficarra, Ernesto Lax
Let be the standard graded polynomial ring, with a field, and let , , be a -tuple…