For P a poset or lattice, let Id(P ) denote the poset, respectively, lattice, of upward directed downsets in P, including the empty set, and let id(P ) = Id(P )−{∅}. This note obtains various results to the effect that Id(P ) is always, and id(P ) often, “essentially larger” than P. In the first vein, we find that a poset P admits no <-respecting map (and so in particular, no one-to-one isotone...

This paper shows that any compactly generated lattice is a subdirect product of subdirectly irreducible lattices which are complete and upper continuous. An example of a compactly generated lattice which cannot be subdirectly decomposed into subdirectly irreducible compactly generated lattices is given. In the case of an ideal lattice of a lattice L, the decomposition into subdirectly irreducib...

Introduction. L. Fuchs [2 ] has given for Noetherian rings a theory of the representation of an ideal as an intersection of primal ideals, the theory being in many ways analogous to the classical Noether theory. An ideal Q is primal if the elements not prime to Q form an ideal, necessarily prime, called the adjoint of Q. Primary ideals are necessarily primal, but not conversely. Analogous resul...

Exploiting the analogy between exemplar models and population coding schemes, we characterize, by means of information theoretic tools, the efficiency of a large but finite population of cells coding for a discrete set of categories (e.g. vowels). The optimal code is shown to typically allocate more cells to class boundaries than to regions further apart. We then discuss the predicted perceptua...

We consider the problem of designing reliable and confidential lattice codes, known as wiretap lattice codes, for fast fading channels. We identify as code design criterion for finite lattice constellations a finite sum of inverse of algebraic norms, in fact the analogous for finite sums of the known criterion for infinite constellations, which motivates us to study totally real number fields w...

Pregnancy and delivery is one of the main causes in the female body weight alteration, especially with obesity. This alteration in body weight has a significant effect not only for a femine beauty standpoint, but also for more important reproductive functions in postpartum. For the actual condition of the maternal body weight alteration and its clinical significance, we made the various analysi...

Let I be a non-zero left ideal of r-ring M satisfying the condition alpha b beta c= c for all a,b,c, e and alpha, r. We show that contains non-trivial central if is semiprime which admits an appropriate derivations on I, also commutative prime admitting centralizing derivation I. next give some characterizations when generalized act as homomorphisms anti-homomorphisms or two-sided ideals gamma ...