Here is the gist of the Eisenbud–Sturmfels paper Binomial ideals, Duke Math. J. 84 (1996), 1–45. The main results are that the associated primes, the primary components, and the radical of a binomial ideal in a polynomial ring are binomial if the base ring is algebraically closed. Throughout, R = k[X1, . . . , Xn], where k is a field and X1, . . . , Xn are variables over k. A monomial is an ele...

One of the sciences used in digital security systems is cryptography. Cryptography closely related to integer system, especially prime numbers. Prime numbers themselves have been abstracted a lot. form abstraction ideal. Previous studies proven that an Ideal said be ideal on if and only I constructed by element. Other also shown how develops. them research result Dauns, where developed submodul...

Let K be an algebraically closed field. For n ≥ 0, let An denote Kn, and let A = K[An] denote K[X1, . . . , Xn]. We refer to An as affine n-space. For any subset S ⊆ An, let I(S) ⊆ A denote the ideal of all polynomials that vanish on S. (For those familiar with Spec, the affine scheme associated to S is Spec(A/I(S)). Note that any ideal I ⊆ A defines an affine subscheme of Spec(A), and ideals I...

in this paper, various elementary properties of vague rings are obtained. furthermore, the concepts of vague subring, vague ideal, vague prime ideal and vague maximal ideal are introduced, and the validity of some relevant classical results in these settings are investigated.

It is a well known theorem that an abelian group G satisfying G = nG for every positive integer n is a direct summand of every abelian group H which contains G as a subgroup. It is the object of this note to generalize this theorem to abelian groups admitting a ring of operators, and to show that the corresponding conditions are not only sufficient but are at the same time necessary. Finally we...

In this paper, we introduce a Sheffer stroke Hilbert algebra by giving definitions of and algebra. After it is shown that the axioms are independent, given some properties algebraic structure. Then stated relationship between defining unary operation on Also, presented deductive system ideal It defined an generated subset algebra, constructed new adding element to its ideal.

We study properties of a poset generating a Cohen-Macaulay algebra with straightening laws (ASL for short). We show that if a poset P generates a Cohen-Macaulay ASL, then P is pure and, if P is moreover Buchsbaum, then P is Cohen-Macaulay. Some results concerning a Rees algebra of an ASL defined by a straightening closed ideal are also established. And it is shown that if P is a Cohen-Macaulay ...

notions of strongly regular, regular and left(right) regular $gamma$−semigroupsare introduced. equivalent conditions are obtained through fuzzy notion for a$gamma$−semigroup to be either strongly regular or regular or left regular.

A linear interpolation scheme is termed ‘ideal’ when its errors form a polynomial ideal. The paper surveys basic facts about ideal interpolation and raises some questions. Ideal interpolation is, by definition, given by a linear projector on the space Π of polynomials whose kernel is a polynomial ideal. It is therefore also any linear map, as used in algebra, that associates a polynomial with i...

This paper presents a 6-element series array quasi-lumped element resonator antenna. The proposed antenna employs an interdigital capacitor in parallel with a straight strip conductor whose center finger is shorted across the capacitor. An array configuration is imperative as the gain of a single quasi-lumped element arrangement was only moderate and specifically put at about 9.4 dBi which may ...