Zero-divisor graph with respect to an ideal

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A note on the countable union of prime submodules

Let M be a finitely-generated module over a Noetherian ring R. Suppose is an ideal of R and let N=M and =Ann(M/N). If ⫅J(R), M is complete with respect to the -adic topology, {Pi}i≥1 is a countable family of prime submodules of M, and x∈M, then x+N⫅∪i≥1Pi implies that x+N⫅Pj for some i≥1. This extends a theorem of Sharp and Vámos concerning prime ideals to prime submodules

La Poliomyelite en Iran Premieres Recherches de Laboratoire

This research work on the status of poliomyelitis in Iran, performed in 1954, in 1958-59, consisted in providing data on the past history of the infection and on its present diffusion in this country. The serological and COprologi~al surveys produced evidence of conditions similar to thos.e of other countries .WIth the same public health situation: large and permanent (WIthout seasonal v~riatlOnSJ diffusion of the e~teroviruses, reaching percentages of 37 to 74% (accol~'dmg to the groups) of ca:rri!ers-excreters in a sampling of healthy chi~dren u~der five y~a!'s of age, providing high levels of early and complete Immunlzation against the pohomyelitic disease

3-Designs with Block Size 6 from PSL(2, q) and Their Large Sets

We investigate the existence of 3-designs and uniform large sets of 3-designs with block size 6 admitting PSL(2, q) as an automorphism group. We show the existence of simple 3-(28, 6, 10m) designs for 1 ≤ m ≤ 230. Most of these designs were previously unknown

Classification of rings with unit graphs having domination number less than four

Dedicated with gratitude to our friend Alberto Facchini on the occasion of his 60th birthday Abstract. Let R be a finite commutative ring with nonzero identity. The unit graph of R is the graph obtained by setting all the elements of R to be the vertices and defining distinct vertices x and y to be adjacent if and only if x + y is a unit element of R. In this paper, a classification of finite commutative rings with nonzero identity in which their unit graphs have domination number less than four is given. 1