We study computational aspects of the tight closure of a homogeneous primary ideal in a two-dimensional normal standard-graded domain. We show how to use slope criteria for the sheaf of syzygies for generators of the ideal to compute its tight closure. In particular, our method gives an algorithm to compute the tight closure of three elements under the condition that we are able to compute the ...

If A is a subset of Z, then the n-th characteristic ideal of A is the fractional ideal of Z consisting of 0 and the leading coe cients of polynomials in Q[x] of degree no more than n which are integer-valued on A. The valuative capacity with respect to a prime p of A is a measure of the rate of growth of the p-adic part of these characteristic ideals of A and is defined, for a given p, to be th...

The ideals of the ring Zp are {0} and pZp, n ≥ 0. From this it follows that Zp is a discrete valuation ring, a principal ideal domain with exactly one maximal ideal, namely pZp; Zp is the valuation ring of Qp with the valuation vp. For n ≥ 1, Zp/pZp is isomorphic as a ring with Z/pZ. |x|p = p−vp(x), dp(x, y) = |x− y|p. With the topology induced by the metric dp, Qp is a locally compact abelian ...

In this correspondence, we present a construction for binary pseudorandom sequences of period 2 1 with ideal autocorrelation property using the polynomial z+(z+1). We show that the sequence obtained from the polynomial becomes an m-sequence for certain values of d. We also find a few values of d which yield new binary sequences with ideal autocorrelation property when m is 3k 1, where k is a po...

We extend the Gröbner basis theory developed in [10, 11] to certain non-homogeneous, locally filtered finitely generated ideals in R0 , and to certain admissible orders. The main tool used is the study of two homogeneous ideals that may be associated to an ideal I R0 , namely the ideal grT (I) generated by all homogenous components of maximal degree of elements in I , and the “homogenized” idea...

An ideal K of R is a subset that is both a left ideal and a right ideal of R. For emphasis, we sometimes call it a two-sided ideal but the reader should understand that unless qualified, the word ideal will always refer to a two-sided ideal. The zero ideal (0) and the whole ring R are examples of two-sided ideals in any ring R. A (left)(right) ideal I such that I 6= R is called a proper (left)(...

1. Results. Scattered results about countably2 generated ideals in C(X) are established in [2] and [4] : Op is countably generated if and only if pEX and p has a countable base of neighborhoods; Op is both prime and countably generated if and only if Mp is principal, and if and only if pEX and p is isolated; no lower prime ideal is countably generated. We generalize these as follows: if Mp is c...

let $r$ be a commutative ring with zero-divisor set $z(r)$. the total graph of $r$, denoted by$t(gamma(r))$, is the simple (undirected) graph with vertex set  $r$ where two distinct vertices areadjacent if their sum lies in $z(r)$.this work considers minimum zero-sum $k$-flows for $t(gamma(r))$.both for $vert rvert$ even and the case when $vert rvert$ is odd and $z(g)$ is an ideal of $r$it is s...

In this paper we exhibit an example of a three-dimensional regular local domain (A,n) having a height-two prime ideal P with the property that the extension P of P to the n-adic completion  of A is not integrally closed. We use a construction we have studied in earlier papers: For R = k[x, y, z], where k is a field of characteristic zero and x, y, z are indeterminates over k, the example A is...

Gromov-Witten, Gopakumar-Vafa, and Donaldson-Thomas invariants of Calabi-Yau threefolds are compared. In certain situations, the Donaldson-Thomas invariants are very easy to handle, sometimes easier than the other invariants. This point is illustrated in several ways, especially by revisiting computations of Gopakumar-Vafa invariants by Katz, Klemm, and Vafa in a rigorous mathematical framework...