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

Zero-divisor graph with respect to an ideal

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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