Abstract. At EUROCRYPT 2011, Gentry and Halevi implemented a variant of Gentry’s fully homomorphic encryption scheme. The core part in their key generation is to generate an odd-determinant ideal lattice having a particular type of Hermite Normal Form. However, they did not give a rigorous proof for the correctness. We present a better key generation algorithm, improving their algorithm from tw...

Chain conditions, finiteness conditions, growth conditions, and other forms of finiteness, Noetherian rings and Artinian rings have been systematically studied for commutative rings and algebras since 1959. In pursuit of the deeper results of ideal theory in ordered groupoids (semigroups), it is necessary to study special classes of ordered groupoids (semigroups). Noetherian ordered groupoids (...

In this study we examined the influence of normative body ideals in the form of perceived peer preferences on personal body ideals and body dissatisfaction Participants (N=146 female college students) were exposed to the purported preferences of peers representing either relatively thin or heavy body ideals. Along with the normative body ideal manipulation, the gender of the purported peers was...

where lm(I) denotes the ideal generated by the leading monomials of the elements of I. This condition has already been studied in Bayer et al. (1991) and it has been shown that (1.1) holds for any ideal and any term order if and only if π is flat. In this paper we study condition (1.1) under the additional assumption that R′ is not a general Noetherian commutative ring with identity but a field...

Let S be a set of n ideals of a commutative ring A and let Geven (respectively Godd) denote the product of all the sums of even (respectively odd) number of ideals of S. If n ≤ 6 the product of Geven and the intersection of all ideals of S is included in Godd. In the case A is an Noetherian integral domain, this inclusion is replaced by equality if and only if A is a Dedekind domain.

The concept of a 0-distributive poset is introduced. It is shown that a section semicomplemented poset is distributive if and only if it is 0-distributive. It is also proved that every pseudocomplemented poset is 0-distributive. Further, 0-distributive posets are characterized in terms of their ideal lattices.

We consider the fuzzification of the notion of implicative hyper BCK-ideals, and then investigate several properties. Using the concept of level subsets, we give a characterization of a fuzzy implicative hyper BCK-ideal. We state a relation between a fuzzy hyper BCK-ideal and a fuzzy implicative hyper BCK-ideal. We establish a condition for a fuzzy hyper BCK-ideal to be a fuzzy implicative hype...

An important predictor of historical sound change, functional load, fails to capture insights from speech perception. Building on ideal observer models of word recognition, we devise a new definition of functional load that incorporates both a priori expectedness and perceptual information. We explore this new measure with a simple model and find that it outperforms tra-

Abstmct-Given a set of parties {l,. , n ) , an access structure is a monotone collection of subsets of the parties. For a certain domain of secrets, a secret-sharing scheme for an access structure is a method for a dealer to distribute shares to the parties. These shares enable subsets in the access structure to reconstruct the secret, while subsets not in the access structure get no informatio...