We characterize the lcm lattices that support a monomial ideal with a pure resolution. Given such a lattice, we provide a construction that yields a monomial ideal with that lcm lattice and whose minimal free resolution is pure.

Abstract We introduce differential primary decompositions for ideals in a commutative ring. Ideal membership is characterized by conditions. The minimal number of conditions needed the arithmetic multiplicity. Minimal are unique up to change bases. Our results generalize construction Noetherian operators analytic theory Ehrenpreis–Palamodov, and they offer concise method representing affine sch...

Describing the properties of the minimal free resolution of a monomial ideal I is a difficult problem posed in the early 1960’s. The main directions of progress on this problem were: • constructing the minimal free resolutions of special monomial ideals, cf. [AHH, BPS] • constructing non-minimal free resolutions; for example, Taylor’s resolution (cf. [Ei, p. 439]) and the cellular resolutions •...

Aim: The laser method (FiLaCTM) has recently emerged as a minimally invasive treatment option in the of anal fistula. Anal incontinence and fistula recurrence after surgery are postoperative problems that complicate treatment. In our study, we aimed to investigate effectiveness film which cases it should be preferred Methods: Twelve patients who underwent FiLaCTM diode at Derik State Hospital b...

‎Let $X=left(‎ ‎begin{array}{llll}‎ ‎ x_1 & ldots & x_{n-1}& x_n\‎ ‎ x_2& ldots & x_n & x_{n+1}‎ ‎end{array}right)$ be the Hankel matrix of size $2times n$ and let $G$ be a closed graph on the vertex set $[n].$ We study the binomial ideal $I_Gsubset K[x_1,ldots,x_{n+1}]$ which is generated by all the $2$-minors of $X$ which correspond to the edges of $G.$ We show that $I_G$ is Cohen-Macaula...

For an $n$-gon with vertices at points $1,2,cdots,n$, the Betti numbers of its suspension, the simplicial complex that involves two more vertices $n+1$ and $n+2$, is known. In this paper, with a constructive and simple proof, wegeneralize this result to find the minimal free resolution and Betti numbers of the $S$-module $S/I$ where  $S=K[x_{1},cdots, x_{n}]$ and $I$ is the associated ideal to ...