Let $(R,m)$ be a commutative Noetherian local ring, $M$ a finitely generated $R$-module of dimension $d$, and let $I$ be an ideal of definition for $M$. In this paper, we extend cite[Corollary 10(4)]{P} and also we show that if $M$ is a Cohen-Macaulay $R$-module and $d=2$, then $lambda(frac{widetilde{I^nM}}{Jwidetilde{I^{n-1}M}})$ does not depend on $J$ for all $ngeq 1$, where $J$ is a minimal ...

Let A = K[x1, . . . , xn] denote the polynomial ring in n variables over a field K with each deg xi = 1. Let I be a homogeneous ideal of A with I 6= A and HA/I the Hilbert function of the quotient algebra A/I. Given a numerical function H : N → N satisfying H = HA/I for some homogeneous ideal I of A, we write AH for the set of those integers 0 ≤ r ≤ n such that there exists a homogeneous ideal ...

Let A be a Noetherian local ring with the maximal ideal m and an m-primary ideal J . Let F = {In}n≥0 be a good filtration of ideals in A. Denote by FJ (F) = ⊕ n≥0 (In/JIn)t n the fiber cone of F with respect to J. The paper characterizes the multiplicity and the CohenMacaulayness of FJ (F) in terms of minimal reductions of F .

For an integer n ≥ 3, the clutter ∆n := { {1, 2}, {1, 3}, . . . , {1, n}, {2, 3, . . . , n} } is called a delta of dimension n, whose members are the lines of a degenerate projective plane. In his seminal paper on non-ideal clutters, Alfred Lehman manifested the role of the deltas as a distinct class of minimally non-ideal clutters [DIMACS, 1990]. A clutter is delta free if it has no delta mino...

then the ideal (F1, ..., FN) they generate in the Paley-Wiener algebra Ê ′(Rn) is slowly decreasing respect to the Paley-Wiener weight p(z) = log |z| + |Im z|. As a consequence, this ideal is closed in Ê ′(Rn). It coincides with the ideal [I(F1, ..., FN)]loc, which consists of elements in Ê ′(Rn) that belong locally to the ideal generated by F1, ..., FN in the algebra of entire functions in n v...

let $s$ be an ordered semigroup. a fuzzy subset of $s$ is anarbitrary mapping   from $s$ into $[0,1]$, where $[0,1]$ is theusual interval of real numbers. in this paper,  the concept of fuzzygeneralized bi-ideals of an ordered semigroup $s$ is introduced.regular ordered semigroups are characterized by means of fuzzy leftideals, fuzzy right ideals and fuzzy (generalized) bi-ideals.finally, two m...

Intravenous hyperalimentation was done in 11 underweight adults whose body weight (body wt) was less than 85 percent of ideal. For the first 6 days, "complete formula" was infused furnishing per kilogram ideal body wt per day: 15 g glucose, 0.40 g N, 0.018 g P, 2.4 meq K, 3.0 meq Na, 2.3 meq C1, 0.5 meq Mg, 0.45 meq Ca, and 50 ml H20. Patients gained weight at an average rate of 9.0 g/kg ideal ...

The study of symmetry is one the most important and beautiful themes uniting various areas contemporary arithmetic. Algebraic structures are useful in pure mathematics for learning a geometrical object’s symmetries. In order to provide mathematical tool dealing with negative information, negative-valued function came into existence along N-structures. present analysis, notion N-structures appli...

This study tested the direct effect of watching thin ideal children's television on body satisfaction in preadolescent girls (6-8 years old). A within-subject design was used in which girls (N = 51) were tested three times. They watched television clips in random order containing either (1) thin ideal animated characters or (2) animated characters with no thin ideal features or (3) 'real' human...

Given two Banach spaces X and Y , we write L(X, Y ) for the space of all continuous linear operators from X to Y . A linear subspace J of L(X, Y ) is said to be an ideal if ATB ∈ J whenever A ∈ L(Y ), T ∈ J , and B ∈ L(X). It is known (see, e.g., Caradus:74 [CPY74]) that the only norm closed ideal in L(lp), 1 6 p < ∞ is the ideal of compact operators. The structure of closed ideals in L(lp ⊕ lq...