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.

About one year ago, it was speculated that decaying or annihilating Light Dark Matter (LDM) particles could explain the flux and extension of the 511 keV line emission in the galactic centre. Here we present a thorough comparison between theoretical expectations of the galactic positron distribution within the LDM scenario and observational data from INTEGRAL/SPI. Unlike previous analyses, ther...

We establish representation types (finite, tame or wild) of finite dimensional Munn algebras with semisimple bases. As an application, we Rees matrix semigroups, in particular, 0-simple and their mutually annihilating unions.

We fully characterize regular Hom-Lie structures on the incidence algebra I(X, K) of a finite connected poset X over field K. prove that such structure is sum central-valued linear map annihilating Jacobson radical with composition certain inner and multiplicative automorphisms K).

BY P . ERDŐS AND P . NEY Hungarian Academy of Sciences and University of Wisconsin Particles perform independent random walks on the integers, and are annihilated if they cross paths or land at the same point. The problem is to determine whether the origin is hit infinitely often . The answer is shown to depend on the initial distribution of particles in accordance with a "log log law ." Severa...

We assign a countable ordinal number to each probability measure which annihilates all H-sets. The descriptive-set theoretic structure of this assignment allows us to show that this class of measures is coanalytic non-Borel. In addition, it allows us to quantify the failure of Rajchman's conjecture. Similar results are obtained for measures annihilating Dirichlet sets. A closet subset E of the ...