Let (A, m) be an excellent normal local ring with algebraically closed residue class field. Given integrally closed m-primary ideals I ⊃ J , we show that there is a composition series between I and J , by integrally closed ideals only. Also we show that any given integrally closed m-primary ideal I, the family of integrally closed ideals J ⊂ I, lA(I/J) = 1 forms an algebraic variety with dimens...

A ring Λ is called a tiled order if Λ is a prime Noetherian semi-prefect semi-distributive ring with non-zero Jacobson radical. Any tiled order can be constructed from a (non-necessarily commutative) discrete valuation ring and an exponent matrix. The latter means a square integer matrix A = (αps), whose diagonal entries are equal to zero, and for all possible indices i, j, k, the following ine...

A conjecture on vanishing and non-negativity of intersection multiplicity on the blow-up of a regular local ring at its closed point has been proposed. Proofs of vanishing, several special cases of non-negativity and a sufficient condition for non-negativity of this conjecture are described. The topic on intersection multiplicity on vector bundles is also addressed. Introduction. Let X be a reg...

Anillin is a conserved protein required for cell division (Field, C.M., and B.M. Alberts. 1995. J. Cell Biol. 131:165-178; Oegema, K., M.S. Savoian, T.J. Mitchison, and C.M. Field. 2000. J. Cell Biol. 150:539-552). One fission yeast homologue of anillin, Mid1p, is necessary for the proper placement of the division site within the cell (Chang, F., A. Woollard, and P. Nurse. 1996. J. Cell Sci. 10...

let $r$ be a ring‎, ‎and let $n‎, ‎d$ be non-negative integers‎. ‎a right $r$-module $m$ is called $(n‎, ‎d)$-projective if $ext^{d+1}_r(m‎, ‎a)=0$ for every $n$-copresented right $r$-module $a$‎. ‎$r$ is called right $n$-cocoherent if every $n$-copresented right $r$-module is $(n+1)$-coprese-nted‎, ‎it is called a right co-$(n,d)$-ring if every right $r$-module is $(n‎, ‎d)$-projective‎. ‎$r$ ...

Dehydro-leucodin [systematic name: (1S,6S,2R)-9,13-dimeth-yl-5-methyl-ene-3-oxatricyclo-[8.3.0.0(2,6)]trideca-9,12-diene-4,11-dione], C(15)H(16)O(3), is a guanolide isolated from Artemisia douglasiana. The fused-ring system contains a seven-membered ring that adopts a chair conformation, a fused planar cyclo-pentenone ring and a five-membered lactone ring fused in envelope conformation. The abs...

We prove a Cohen-Macaulay version of result by Avramov-Golod and Frankild-J{\o}rgensen about Gorenstein rings, showing that if noetherian ring $A$ is Cohen-Macaulay, $a_1,\dots,a_n$ any sequence elements in $A$, then the Koszul complex $K(A;a_1,\dots,a_n)$ DG-ring. further generalize this result, it also holds for commutative DG-rings. In process proving this, we develop new technique to study ...

We present algorithms which, given a genus 2 curve C defined over a finite field and a quartic CM field K, determine whether the endomorphism ring of the Jacobian J of C is the full ring of integers in K. In particular, we present probabilistic algorithms for computing the field of definition of, and the action of Frobenius on, the subgroups J [l] for prime powers l. We use these algorithms to ...

The lio gene encodes a putative receptor tyrosine kinase, with unique motifs both in the extracellular and catalytic domains (Dura, J.-M., Préat, T., Tully, T., 1993. Identification of linotte, a new gene affecting learning and memory in Drosophila melanogaster. J. Neurogenet. 9, 1-14). We show here that a complete deletion of lio activity causes specific structural defects in the adult brain. ...

the zero-divisor graph of a commutative ring r with respect to nilpotent elements is a simple undirected graph $gamma_n^*(r)$ with vertex set z_n(r)*, and two vertices x and y are adjacent if and only if xy is nilpotent and xy is nonzero, where z_n(r)={x in r: xy is nilpotent, for some y in r^*}. in this paper, we investigate the basic properties of $gamma_n^*(r)$. we discuss when it will be eu...