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.

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-

Water erosion causes severe soil damage in northern forests of Iran which is associated with different rut depths in skid trails. The aim of this study was to assess rutting and soil displacement on skid trails to mitigate water erosion. Therefore the research was carried out in eight parcels of district No 3 of Shafarood Forest in the North of Iran. In order to evaluate the amount of erosion i...

t-condylar fracture of the distal humerus is rare in the skeletally immature children and is very rare in young children, under 9 years of age. this fracture has been classified  as:  type a ( minimally displaced or undisplaced), type b (displaced  but  not comminuted ) and type c (displaced and comminuted). herein, we report a t-condylar fracture of the distal humerus in a 5-yr-old boy. this f...